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%I A285017 #42 Jul 31 2017 03:22:51
%S A285017 43,73,157,211,241,421,463,601,757,1123,1483,2551,2971,3307,3907,4423,
%T A285017 4831,5701,6007,6163,6481,8191,9901,11131,12211,12433,13807,14281,
%U A285017 19183,20023,20593,21757,22621,22651,23563,24181,26083,26407,27061,28393,31153,35533
%N A285017 Primes of the form  1 + n + n^2 + n^3 + ... + n^k, n > 1, k > 1 where n is not prime.
%C A285017 These numbers are Brazilian primes belonging to A085104.
%C A285017 Brazilian primes with n prime are A023195, except 3 which is not Brazilian.
%C A285017 A085104 = This sequence Union { A023195 \ number 3 }.
%C A285017 k + 1 is necessarily prime, but that's not sufficient: 1 + 10 + 100 = 111.
%C A285017 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.
%C A285017 Number of terms < 10^k: 0, 2, 9, 23, 64, 171, 477, 1310, 3573, 10098, ..., . - _Robert G. Wilson v_, Apr 15 2017
%H A285017 Chai Wah Wu, <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL0EyODUwMTcvYjI4NTAxNy50eHQ">Table of n, a(n) for n = 1..10000</a> (terms 1..1310 from Robert G. Wilson v)
%H A285017 Bernard Schott, <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL0ExMjUxMzQvYTEyNTEzNC5wZGY">Les nombres brésiliens</a>, Reprinted from Quadrature, no. 76, April-June 2010, pages 30-38, included here with permission from the editors of Quadrature.
%e A285017 157 = 12^2 + 12 + 1 = 111_12 is prime and 12 is composite.
%p A285017 N:= 40000: # to get all terms <= N
%p A285017 res:= NULL:
%p A285017 for k from 2 to ilog2(N) do if isprime(k) then
%p A285017   for n from 2 do
%p A285017     p:= (n^(k+1)-1)/(n-1);
%p A285017     if p > N then break fi;
%p A285017     if isprime(p) and not isprime(n) then res:= res, p fi
%p A285017 od fi od:
%p A285017 res:= {res}:
%p A285017 sort(convert(res,list)); # _Robert Israel_, Apr 14 2017
%t A285017 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 *)
%o A285017 (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
%o A285017 (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
%Y A285017 Cf. A002383, A023195, A053183, A053696, A085104, A088548, A088550, A185632, A190527, A194257.
%K A285017 nonn
%O A285017 1,1
%A A285017 _Bernard Schott_, Apr 08 2017

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