%I #25 Jul 22 2021 23:52:37

%S 1,6,14,26,38,40,46,56,60,66,68,72,80,87,93,95,115,122,126,128,146,

%T 156,158,160,180,186,192,203,206,208,220,221,235,237,238,264,266,280,

%U 282,290,294,300,303,320,341,350,363,381,395,399,404,405,417,418,436,438,447,450

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

%C A163268 Union {This sequence} = A100330.

%C 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.

%H Chai Wah Wu, <a href="/A288939/b288939.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%t Select[Range@ 450, And[! PrimeQ@ #, PrimeQ@ Total[#^Range[0, 6]]] &] (* _Michael De Vlieger_, Jun 19 2017 *)

%o (PARI) isok(n) = !isprime(n) && isprime(1+n+n^2+n^3+n^4+n^5+n^6); \\ _Michel Marcus_, Jun 19 2017

%o (Python)

%o from sympy import isprime

%o 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

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

%K nonn

%O 1,2

%A _Bernard Schott_, Jun 19 2017