cp's OEIS Frontend

A247966 Primes p such that the polynomial k^4 + k^3 + k^2 + k + p yields only primes for k = 0...6.

%I A247966 #29 Jan 10 2017 10:49:53
%S A247966 43,457,967,1093,5923,8233,11923,15787,41113,80683,151783,210127,
%T A247966 213943,294919,392737,430879,495559,524827,537007,572629,584557,
%U A247966 711727,730633,731593,1097293,1123879,1138363,1149163,1396207,1601503,1739557,1824139,2198407,2223853
%N A247966 Primes p such that the polynomial k^4 + k^3 + k^2 + k + p yields only primes for k = 0...6.
%H A247966 K. D. Bajpai, <a href="/A247966/b247966.txt">Table of n, a(n) for n = 1..1405</a>
%e A247966 a(1) = 43:
%e A247966 0^4 + 0^3 + 0^2 + 0 + 43 = 43;
%e A247966 1^4 + 1^3 + 1^2 + 1 + 43 = 47;
%e A247966 2^4 + 2^3 + 2^2 + 2 + 43 = 73;
%e A247966 3^4 + 3^3 + 3^2 + 3 + 43 = 163;
%e A247966 4^4 + 4^3 + 4^2 + 4 + 43 = 383;
%e A247966 5^4 + 5^3 + 5^2 + 5 + 43 = 823;
%e A247966 6^4 + 6^3 + 6^2 + 6 + 43 = 1597;
%e A247966 all seven are primes.
%t A247966 Select[f=k^4 + k^3 + k^2 + k; k = {0, 1, 2, 3, 4, 5, 6}; Prime[Range[2000000]], And @@ PrimeQ[#+f] &]
%t A247966 Select[Prime[Range[200000]],AllTrue[#+{4,30,120,340,780,1554},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jan 10 2017 *)
%o A247966 (PARI) forprime(p=1, 1e6, if( isprime(p+0)& isprime(p+4)& isprime(p+30)& isprime(p+120)& isprime(p+340)& isprime(p+780)&  isprime(p+1554), print1(p,", ")))
%Y A247966 Cf. A144051, A187057, A187058, A187060, A190800, A191456, A191457, A191458.
%K A247966 nonn
%O A247966 1,1
%A A247966 _K. D. Bajpai_, Jan 11 2015