cp's OEIS Frontend

A288939 Nonprime numbers k such that k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 is prime.

%I A288939 #25 Jul 22 2021 23:52:37
%S A288939 1,6,14,26,38,40,46,56,60,66,68,72,80,87,93,95,115,122,126,128,146,
%T A288939 156,158,160,180,186,192,203,206,208,220,221,235,237,238,264,266,280,
%U A288939 282,290,294,300,303,320,341,350,363,381,395,399,404,405,417,418,436,438,447,450
%N A288939 Nonprime numbers k such that k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 is prime.
%C A288939 A163268 Union {This sequence} = A100330.
%C A288939 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 A288939 Chai Wah Wu, <a href="/A288939/b288939.txt">Table of n, a(n) for n = 1..10000</a>
%e A288939 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 A288939 for n from 1 to 200 do s(n):= 1+n+n^2+n^3+n^4+n^5+n^6;
%p A288939 if not isprime(n) and isprime(s(n)) then print(n,s(n)) else fi; od:
%t A288939 Select[Range@ 450, And[! PrimeQ@ #, PrimeQ@ Total[#^Range[0, 6]]] &] (* _Michael De Vlieger_, Jun 19 2017 *)
%o A288939 (PARI) isok(n) = !isprime(n) && isprime(1+n+n^2+n^3+n^4+n^5+n^6); \\ _Michel Marcus_, Jun 19 2017
%o A288939 (Python)
%o A288939 from sympy import isprime
%o A288939 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 A288939 Cf. A053716, A085104, A088550, A100330, A163268, A194194, A194257, A285017.
%K A288939 nonn
%O A288939 1,2
%A A288939 _Bernard Schott_, Jun 19 2017