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A247949 Primes p such that the polynomial k^4 + k^3 + k^2 + k + p yields only primes for k = 0...5.

%I A247949 #34 Dec 24 2023 16:07:50
%S A247949 7,43,79,457,877,967,1093,2437,2683,3187,5077,5923,7933,8233,11923,
%T A247949 12889,15787,17389,19993,31543,41113,41617,42457,71359,77863,80683,
%U A247949 91393,101719,102643,105967,107347,120163,129733,137593,151783,170263,175723,197569,210127
%N A247949 Primes p such that the polynomial k^4 + k^3 + k^2 + k + p yields only primes for k = 0...5.
%C A247949 All terms == 1 mod 6. - _Robert Israel_, Jan 11 2015
%H A247949 K. D. Bajpai, <a href="/A247949/b247949.txt">Table of n, a(n) for n = 1..6730</a>
%e A247949 a(1) = 7:
%e A247949 0^4 + 0^3 + 0^2 + 0 + 7 = 7;
%e A247949 1^4 + 1^3 + 1^2 + 1 + 7 = 11;
%e A247949 2^4 + 2^3 + 2^2 + 2 + 7 = 37;
%e A247949 3^4 + 3^3 + 3^2 + 3 + 7 = 127;
%e A247949 4^4 + 4^3 + 4^2 + 4 + 7 = 347;
%e A247949 5^4 + 5^3 + 5^2 + 5 + 7 = 787;
%e A247949 all six are primes.
%p A247949 select(p -> andmap(isprime, [p, p+4, p+30, p+120, p+340, p+780]), [seq(6*i+1, i=1..10^5)]); # _Robert Israel_, Jan 11 2015
%t A247949 Select[f=k^4 + k^3 + k^2 + k; k = {0, 1, 2, 3, 4, 5}; Prime[Range[2000000]], And @@ PrimeQ[#+f] &]
%t A247949 Select[Prime[Range[20000]],AllTrue[#+{4,30,120,340,780},PrimeQ]&] (* _Harvey P. Dale_, Dec 24 2023 *)
%o A247949 (PARI) forprime(p=1, 500000, if( isprime(p+0)& isprime(p+4)& isprime(p+30)& isprime(p+120)& isprime(p+340)& isprime(p+780), print1(p,", ")))
%Y A247949 Cf. A144051, A187057, A187058, A187060, A190800, A191456, A191457, A191458.
%K A247949 nonn
%O A247949 1,1
%A A247949 _K. D. Bajpai_, Jan 11 2015