A088550 -id:A088550

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A085104

Primes of the form 1 + n + n^2 + n^3 + ... + n^k, n > 1, k > 1.

+10
66

7, 13, 31, 43, 73, 127, 157, 211, 241, 307, 421, 463, 601, 757, 1093, 1123, 1483, 1723, 2551, 2801, 2971, 3307, 3541, 3907, 4423, 4831, 5113, 5701, 6007, 6163, 6481, 8011, 8191, 9901, 10303, 11131, 12211, 12433, 13807, 14281, 17293, 19183, 19531, 20023

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Primes that are base-b repunits with three or more digits for at least one b >= 2: Primes in A053696. Subsequence of A000668 U A076481 U A086122 U A165210 U A102170 U A004022 U ... (for each possible b). - Rick L. Shepherd, Sep 07 2009

From Bernard Schott, Dec 18 2012: (Start)

Also known as Brazilian primes. The primes that are not Brazilian primes are in A220627.

The number of terms k+1 is always an odd prime, but this is not enough to guarantee a prime, for example 111 = 1 + 10 + 100 = 3*37.

The inverses of the Brazilian primes form a convergent series; the sum is slightly larger than 0.33 (see Theorem 4 of Quadrature article in the Links). (End)

It is not known whether there are infinitely many Brazilian primes. See A002383. - Bernard Schott, Jan 11 2013

Primes of the form (n^p - 1)/(n - 1), where p is odd prime and n > 1. - Thomas Ordowski, Apr 25 2013

Number of terms less than 10^n: 1, 5, 14, 34, 83, 205, 542, 1445, 3880, 10831, 30699, 88285, ..., . - Robert G. Wilson v, Mar 31 2014

From Bernard Schott, Apr 08 2017: (Start)

Brazilian primes fall into two classes:

1) when n is prime, we get sequence A023195 except 3 which is not Brazilian,

2) when n is composite, we get sequence A285017. (End)

The conjecture proposed in Quadrature "No Sophie Germain prime is Brazilian (prime)" (see link Bernard Schott, Quadrature, Conjecture 1, page 36) is false. Thanks to Giovanni Resta, who found that a(856) = 28792661 = 1 + 73 + 73^2 + 73^3 + 73^4 = (11111)_73 is the 141385th Sophie Germain prime. - Bernard Schott, Mar 08 2019

REFERENCES

Daniel Lignon, Dictionnaire de (presque) tous les nombres entiers, Ellipses, Paris, 2012, page 174.

LINKS

Jon E. Schoenfield, Table of n, a(n) for n = 1..10831 (terms up to 10^10; terms 1..3880 from T. D. Noe)

Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature.

FORMULA

A010051(a(n)) * A088323(a(n)) > 1. - Reinhard Zumkeller, Jan 22 2014

EXAMPLE

13 is a term since it is prime and 13 = 1 + 3 + 3^2 = 111_3.

31 is a term since it is prime and 31 = 1 + 2 + 2^2 + 2^3 + 2^4 = 11111_2.

From Hartmut F. W. Hoft, May 08 2017: (Start)

The sequence represented as a sparse matrix with the k-th column indexed by A006093(k+1), primes minus 1, and row n by A000027(n+1). Traversing the matrix by counterdiagonals produces a non-monotone ordering.

2 4 6 10 12 16

2 7 31 127 - 8191 131071

3 13 - 1093 - 797161 -

4 - - - - - -

5 31 - 19531 12207031 305175781 -

6 43 - 55987 - - -

7 - 2801 - - 16148168401 -

8 73 - - - - -

9 - - - - - -

10 - - - - - -

11 - - - - - 50544702849929377

12 157 22621 - - - -

13 - 30941 5229043 - - -

14 211 - 8108731 - - -

15 241 - - - - -

16 - - - - - -

17 307 88741 25646167 2141993519227 - -

18 - - - - - -

19 - - - - - -

20 421 - - 10778947368421 - 689852631578947368421

21 463 - - 17513875027111 - 1502097124754084594737

22 - 245411 - - - -

23 - 292561 - - - -

24 601 346201 - - - -

Except for the initial values in the respective sequences the rows and columns as labeled in the matrix are:

column 2: A002383 row 2: A000668

column 4: A088548 row 3: A076481

column 6: A088550 row 4: -

column 10: A162861 row 5: A086122.

(End)

MATHEMATICA

max = 140; maxdata = (1 - max^3)/(1 - max); a = {}; Do[i = 1; While[i = i + 2; cc = (1 - m^i)/(1 - m); cc <= maxdata, If[PrimeQ[cc], a = Append[a, cc]]], {m, 2, max}]; Union[a] (* Lei Zhou, Feb 08 2012 *)

f[n_] := Block[{i = 1, d, p = Prime@ n}, d = Rest@ Divisors[p - 1]; While[ id = IntegerDigits[p, d[[i]]]; id != Reverse@ id || Union@ id != {1}, i++]; d[[i]]]; Select[ Range[2, 60], 1 + f@# != Prime@# &] (* Robert G. Wilson v, Mar 31 2014 *)

PROG

(PARI) list(lim)=my(v=List(), t, k); for(n=2, sqrt(lim), t=1+n; k=1; while((t+=n^k++)<=lim, if(isprime(t), listput(v, t)))); vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Jan 08 2013

(PARI) A085104_vec(N, L=List())=forprime(K=3, logint(N+1, 2), for(n=2, sqrtnint(N-1, K-1), isprime((n^K-1)\(n-1))&&listput(L, (n^K-1)\(n-1)))); Set(L) \\ M. F. Hasler, Jun 26 2018

(Haskell)

a085104 n = a085104_list !! (n-1)

a085104_list = filter ((> 1) . a088323) a000040_list

-- Reinhard Zumkeller, Jan 22 2014

CROSSREFS

Cf. A189891 (complement), A125134 (Brazilian numbers), A220627 (Primes that are non-Brazilian).

Cf. A003424 (n restricted to prime powers).

Cf. A053696, A086930, A059055.

Equals A023195 \3 Union A285017 with empty intersection.

Primes of the form (b^k-1)/(b-1) for b=2: A000668, b=3: A076481, b=5: A086122, b=6: A165210, b=7: A102170, b=10: A004022.

Primes of the form (b^k-1)/(b-1) for k=3: A002383, k=5: A088548, k=7: A088550, k=11: A162861.

KEYWORD

nonn,base

AUTHOR

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 03 2003

EXTENSIONS

More terms from David Wasserman, Jan 26 2005

STATUS

approved

A100330

Positive integers k such that k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 is prime.

+10
37

1, 2, 3, 5, 6, 13, 14, 17, 26, 31, 38, 40, 46, 56, 60, 61, 66, 68, 72, 73, 80, 87, 89, 93, 95, 115, 122, 126, 128, 146, 149, 156, 158, 160, 163, 180, 186, 192, 203, 206, 208, 220, 221, 235, 237, 238, 251, 264, 266, 280, 282, 290, 294, 300, 303, 320, 341, 349, 350

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The corresponding primes are A088550. - Bernard Schott, Dec 20 2012

k = 5978493 * 2^150006 - 1 is an example of a very large term of this sequence. The generated prime is proved by the N-1 method (because k is prime and k*(k+1) is fully factored and this provides for an exactly 33.33...% factorization for Phi_7(k) - 1). - Serge Batalov, Mar 13 2015

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

EXAMPLE

2 is in the sequence because 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2 + 1 = 127, which is prime.

MAPLE

A100330 := proc(n)

option remember;

local a;

if n = 1 then

else

for a from procname(n-1)+1 do

if isprime(numtheory[cyclotomic](7, a)) then

return a;

end if;

end do:

end if;

end proc:

seq(A100330(n), n=1..30) ; # R. J. Mathar, Feb 07 2014

MATHEMATICA

Select[Range[350], PrimeQ[Sum[ #^i, {i, 0, 6}]] &] (* Ray Chandler, Nov 17 2004 *)

Do[If[PrimeQ[n^6 + n^5 + n^4 + n^3 + n^2 + n + 1], Print[n]], {n, 1, 500}] (* Vincenzo Librandi, Feb 08 2014 *)

PROG

(Magma) [n: n in [1..500]| IsPrime(n^6 + n^5 + n^4 + n^3 + n^2 + n + 1)]; // Vincenzo Librandi, Feb 08 2014

(PARI) is(n)=isprime(polcyclo(7, n)) \\ Charles R Greathouse IV, Apr 28 2015

CROSSREFS

Cf. A100331, A250174 (Phi_14(n) = n^6 - n^5 + n^4 - n^3 + n^2 - n + 1 primes; these two sequences can also be considered an extension of each other into negative n values), A250177 (Phi_21(n) primes).

KEYWORD

nonn

AUTHOR

Ray G. Opao, Nov 16 2004

STATUS

approved

A088548

Primes of the form k^4 + k^3 + k^2 + k + 1.

+10
14

5, 31, 2801, 22621, 30941, 88741, 245411, 292561, 346201, 637421, 732541, 837931, 2625641, 3500201, 3835261, 6377551, 15018571, 16007041, 21700501, 28792661, 30397351, 35615581, 39449441, 48037081, 52822061, 78914411, 97039801, 147753211, 189004141, 195534851

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

These numbers when >= 31 are primes repunits 11111_n in a base n >= 2, so except 5, they are all Brazilian primes belonging to A085104. (See Links "Les nombres brésiliens", § V.4 - § V.5.) A008858 is generated by the bases n present in A049409. - Bernard Schott, Dec 19 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature.

FORMULA

A000040 intersect A053699. - R. J. Mathar, Feb 07 2014

EXAMPLE

a(2) = 31 is prime and 31 = 2^4 + 2^3 + 2^2 + 2 + 1.

MATHEMATICA

lst={}; Do[a=1+n+n^2+n^3+n^4; If[PrimeQ[a], AppendTo[lst, a]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 02 2009 *)

Select[Table[n^4+n^3+n^2+n+1, {n, 0, 2000}], PrimeQ] (* Vincenzo Librandi, Jul 16 2012 *)

PROG

(PARI) polypn(n, p) = { for(x=1, n, if(p%2, y=2, y=1); for(m=1, p, y=y+x^m; ); if(isprime(y), print1(y", ")); ) }

(Magma) [a: n in [0..200] | IsPrime(a) where a is n^4+n^3+n^2+n+1]; // Vincenzo Librandi, Jul 16 2012

(Python)

from sympy import isprime

print(list(filter(isprime, (k**4+k**3+k**2+k+1 for k in range(120))))) # Michael S. Branicky, May 31 2021

CROSSREFS

Cf. A002383, A049409, A085104, A088550.

KEYWORD

nonn,easy

AUTHOR

Cino Hilliard, Nov 17 2003

STATUS

approved

A285017

Primes of the form 1 + n + n^2 + n^3 + ... + n^k, n > 1, k > 1 where n is not prime.

+10
7

43, 73, 157, 211, 241, 421, 463, 601, 757, 1123, 1483, 2551, 2971, 3307, 3907, 4423, 4831, 5701, 6007, 6163, 6481, 8191, 9901, 11131, 12211, 12433, 13807, 14281, 19183, 20023, 20593, 21757, 22621, 22651, 23563, 24181, 26083, 26407, 27061, 28393, 31153, 35533

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

These numbers are Brazilian primes belonging to A085104.

Brazilian primes with n prime are A023195, except 3 which is not Brazilian.

A085104 = This sequence Union { A023195 \ number 3 }.

k + 1 is necessarily prime, but that's not sufficient: 1 + 10 + 100 = 111.

Most of these terms come from A185632 which are prime numbers 111_n with n no prime, the first other term is 22621 = 11111_12, the next one is 245411 = 11111_22.

Number of terms < 10^k: 0, 2, 9, 23, 64, 171, 477, 1310, 3573, 10098, ..., . - Robert G. Wilson v, Apr 15 2017

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..1310 from Robert G. Wilson v)

Bernard Schott, Les nombres brésiliens, Reprinted from Quadrature, no. 76, April-June 2010, pages 30-38, included here with permission from the editors of Quadrature.

EXAMPLE

157 = 12^2 + 12 + 1 = 111_12 is prime and 12 is composite.

MAPLE

N:= 40000: # to get all terms <= N

res:= NULL:

for k from 2 to ilog2(N) do if isprime(k) then

for n from 2 do

p:= (n^(k+1)-1)/(n-1);

if p > N then break fi;

if isprime(p) and not isprime(n) then res:= res, p fi

od fi od:

res:= {res}:

sort(convert(res, list)); # Robert Israel, Apr 14 2017

MATHEMATICA

mx = 36000; g[n_] := Select[Drop[Accumulate@Table[n^ex, {ex, 0, Log[n, mx]}], 2], PrimeQ]; k = 1; lst = {}; While[k < Sqrt@mx, If[CompositeQ@k, AppendTo[lst, g@k]; lst = Sort@Flatten@lst]; k++]; lst (* Robert G. Wilson v, Apr 15 2017 *)

PROG

(PARI) isok(n) = {if (isprime(n), forcomposite(b=2, n, d = digits(n, b); if ((#d > 2) && (vecmin(d) == 1) && (vecmax(d)== 1), return(1)); ); ); return(0); } \\ Michel Marcus, Apr 09 2017

(PARI) A285017_vec(n)={my(h=vector(n, i, 1), y, c, z=4, L:list); L=List(); forprime(x=3, , forcomposite(m=z, x-1, y=digits(x, m); if((y==h[1..#y])&&2<#y, listput(L, x); z=m; if(c++==n, return(Vec(L))))))} \\ R. J. Cano, Apr 18 2017

CROSSREFS

Cf. A002383, A023195, A053183, A053696, A085104, A088548, A088550, A185632, A190527, A194257.

KEYWORD

nonn

AUTHOR

Bernard Schott, Apr 08 2017

STATUS

approved

A194257

Primes of the form p^6 + p^5 + p^4 + p^3 + p^2 + p + 1 when p is prime.

+10
6

127, 1093, 19531, 5229043, 25646167, 917087137, 52379047267, 153436090543, 502628805631, 11016462577051, 18871143464293, 251059142817757, 1812169199976451, 1940350890330343

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

These primes are generated by exactly A163268.

This sequence is included in A088550.

These numbers are repunit primes 1111111_n, so they are Brazilian primes and are terms of A085104.

Subsequence of A088550. - Hartmut F. W. Hoft, May 05 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A193574(A163268(n)^6). - Hartmut F. W. Hoft, May 08 2017

MAPLE

select(isprime, map(p -> add(p^i, i=0..6), select(isprime, [2, seq(i, i=3..1000, 2)]))); # Robert Israel, May 05 2017

MATHEMATICA

a194257[n_] := Select[Map[(Prime[#]^7-1)/(Prime[#]-1)&, Range[n]], PrimeQ]

a194257[70] (* data *) (* Hartmut F. W. Hoft, May 05 2017 *)

Select[Table[Total[p^Range[0, 6]], {p, Prime[Range[100]]}], PrimeQ] (* Harvey P. Dale, Mar 09 2024 *)

CROSSREFS

Cf. A085104, A088550, A100330, A163268.

KEYWORD

nonn

AUTHOR

Bernard Schott, Dec 21 2012

STATUS

approved

A163268

Primes p such that 1 + p + p^2 + p^3 + p^4 + p^5 + p^6 is prime.

+10
5

2, 3, 5, 13, 17, 31, 61, 73, 89, 149, 163, 251, 349, 353, 461, 523, 599, 647, 863, 941, 947, 1087, 1117, 1229, 1277, 1291, 1297, 1409, 1439, 1489, 1567, 1579, 1609, 1627, 1753, 1783, 1831, 2039, 2131, 2293, 2531, 2609, 2753, 2861, 3037, 3163, 3167, 3299

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Primes in A100330. The generated prime numbers are exactly A194257. [Bernard Schott, Dec 21 2012]

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000 (first 102 terms from Zak Seidov)

MAPLE

select(p -> isprime(p) and isprime(1+p+p^2+p^3+p^4+p^5+p^6), [2, seq(i, i=3..10000, 2)]); # Robert Israel, May 05 2017

MATHEMATICA

f[n_]:=1+n+n^2+n^3+n^4+n^5+n^6; lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n, 7!}]; lst

Select[Prime[Range[500]], PrimeQ[Total[#^Range[0, 6]]]&] (* Harvey P. Dale, Jul 13 2022 *)

PROG

(PARI) n=0; forprime(p=2, 10000, isprime((p^7-1)/(p-1))&&print(n++" "p))\\ Zak Seidov, Mar 09 2013

CROSSREFS

Cf. A053182, A065509, A088550, A100330, A163268, A194257.

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jul 24 2009

EXTENSIONS

Edited (but not checked) by N. J. A. Sloane, Jul 25 2009

STATUS

approved

A245393

Primes of the form m^10 - m^9 + m^8 - m^7 + m^6 - m^5 + m^4 - m^3 + m^2 - m + 1.

+10
4

683, 51828151, 57154490053, 128011456717, 39700406579747, 60867245726761, 135938684703251, 2681921038140191, 825977153711699903, 2411248431216834661, 38518333422551932951, 161352769633614478921, 4679818035765747188623, 10926823630072049689441, 13158906479414390795167

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

All the terms in this sequence are primes, but none are congruent to 9 mod 10.

The value of first few m's corresponding to primes listed in data section are: 2, 6, 12, 13, 23, 24, 26, 35, 62, 69, 91, 105, 147, 160, 163, 183, 185, 193... 469, 491, 492 .....

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..9538

EXAMPLE

m:=2: m^10 - m^9 + m^8 - m^7 + m^6 - m^5 + m^4 - m^3 + m^2 - m + 1 = 683, which is prime, hence appears in the sequence.

m:=6: m^10 - m^9 + m^8 - m^7 + m^6 - m^5 + m^4 - m^3 + m^2 - m + 1 = 51828151, which is prime, hence appears in the sequence.

MATHEMATICA

Select[Table[n^10 - n^9 + n^8 - n^7 + n^6 - n^5 + n^4 - n^3 + n^2 - n + 1, {n, 200}], PrimeQ]

PROG

(PARI)

for(n=1, 10^3, s=sum(i=0, 10, (-n)^i); if(ispseudoprime(s), print1(s, ", "))) \\ Derek Orr, Jul 30 2014

CROSSREFS

Cf. A000040, A088550, A162861.

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Jul 21 2014

STATUS

approved

A194194

Primes of the form n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 where n is nonprime.

+10
3

7, 55987, 8108731, 321272407, 3092313043, 4201025641, 9684836827, 31401724537, 47446779661, 83925549247, 100343116693, 141276239497, 265462278481, 438668366137, 654022685443, 742912017121, 2333350772341, 3324554405047, 4033516174507, 4432676798593, 9752186278927, 14505760086637, 15656690128843, 16882733081761

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Subset of A088550. The n in A018252 for which n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 are prime begin 1, 6, 14, 26, 38, 40.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

a(1) = 1^6 + 1^5 + 1^4 + 1^3 + 1^2 + 1 + 1 = 7.

a(2) = 6^6 + 6^5 + 6^4 + 6^3 + 6^2 + 6 + 1 = 55987.

a(3) = 14^6 + 14^5 + 14^4 + 14^3 + 14^2 + 14 + 1 = 8108731.

a(4) = 26^6 + 26^5 + 26^4 + 26^3 + 26^2 + 26 + 1 = 321272407.

MATHEMATICA

With[{nn=200}, Select[Total[#^Range[0, 6]]&/@Complement[Range[nn], Prime[ Range[PrimePi[nn]]]], PrimeQ]] (* Harvey P. Dale, Nov 15 2013 *)

CROSSREFS

Cf, A000040, A018252, A088548, A185632, A192321.

KEYWORD

nonn,easy

AUTHOR

Jonathan Vos Post, Dec 20 2012

STATUS

approved

A245427

Primes of the form n^6 - n^5 + n^4 - n^3 + n^2 - n + 1.

+10
2

43, 547, 909091, 1623931, 7027567, 10678711, 15790321, 22796593, 32222107, 81867661, 183458857, 234750601, 574995877, 2498207293, 6177695707, 7095062437, 9272716111, 13564461457, 19397579293, 24344094727, 50689400581, 81420308971, 137405657593, 149289169177

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

All the terms in this sequence are primes, but none are congruent to 9 mod 10.

All terms == 1 (mod 7). - Robert Israel, Jul 22 2014

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..13520

EXAMPLE

n = 2: n^6 - n^5 + n^4 - n^3 + n^2 - n + 1 = 43, which is prime.

n = 10: n^6 - n^5 + n^4 - n^3 + n^2 - n + 1 = 909091, which is prime.

MATHEMATICA

Select[Table[n^6 - n^5 + n^4 - n^3 + n^2 - n + 1, {n, 200}], PrimeQ]

CROSSREFS

Cf. A000040, A088550, A162861, A245393.

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Jul 21 2014

STATUS

approved

A288939

Nonprime numbers k such that k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 is prime.

+10
2

1, 6, 14, 26, 38, 40, 46, 56, 60, 66, 68, 72, 80, 87, 93, 95, 115, 122, 126, 128, 146, 156, 158, 160, 180, 186, 192, 203, 206, 208, 220, 221, 235, 237, 238, 264, 266, 280, 282, 290, 294, 300, 303, 320, 341, 350, 363, 381, 395, 399, 404, 405, 417, 418, 436, 438, 447, 450

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

A163268 Union {This sequence} = A100330.

The corresponding prime numbers k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 = 1111111_k are in A194194; all these Brazilian primes belong to A085104 and A285017.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

EXAMPLE

6 is in the sequence because 6^6 + 6^5 + 6^4 + 6^3 + 6^2 + 6 + 1 = 1111111_6 = 55987 which is prime.

MAPLE

for n from 1 to 200 do s(n):= 1+n+n^2+n^3+n^4+n^5+n^6;

if not isprime(n) and isprime(s(n)) then print(n, s(n)) else fi; od:

MATHEMATICA

Select[Range@ 450, And[! PrimeQ@ #, PrimeQ@ Total[#^Range[0, 6]]] &] (* Michael De Vlieger, Jun 19 2017 *)

PROG

(PARI) isok(n) = !isprime(n) && isprime(1+n+n^2+n^3+n^4+n^5+n^6); \\ Michel Marcus, Jun 19 2017

(Python)

from sympy import isprime

A288939_list = [n for n in range(10**3) if not isprime(n) and isprime(n*(n*(n*(n*(n*(n + 1) + 1) + 1) + 1) + 1) + 1)] # Chai Wah Wu, Jul 13 2017

CROSSREFS

Cf. A053716, A085104, A088550, A100330, A163268, A194194, A194257, A285017.

KEYWORD

nonn

AUTHOR

Bernard Schott, Jun 19 2017

STATUS

approved

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