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A253915 Primes p such that the polynomial k^4 + k^3 + k^2 + k + p yields primes for k = 0..8, but not for k = 9.

%I A253915 #45 Sep 11 2021 02:53:02
%S A253915 43,967,11923,213943,2349313,3316147,30637567,33421159,39693817,
%T A253915 49978447,105963769,143405887,148248949,153756073,156871549,172981279,
%U A253915 187310803,196726693,203625283,211977523,220825453,268375879,350968543,357834283,414486697,427990369
%N A253915 Primes p such that the polynomial k^4 + k^3 + k^2 + k + p yields primes for k = 0..8, but not for k = 9.
%C A253915 All the terms in this sequence are congruent to 1 (mod 3).
%H A253915 Jon E. Schoenfield, <a href="/A253915/b253915.txt">Table of n, a(n) for n = 1..155</a> (terms < 2*10^10)
%e A253915 a(1) = 43:
%e A253915 0^4 + 0^3 + 0^2 + 0 + 43 =   43;
%e A253915 1^4 + 1^3 + 1^2 + 1 + 43 =   47;
%e A253915 2^4 + 2^3 + 2^2 + 2 + 43 =   73;
%e A253915 3^4 + 3^3 + 3^2 + 3 + 43 =  163;
%e A253915 4^4 + 4^3 + 4^2 + 4 + 43 =  383;
%e A253915 5^4 + 5^3 + 5^2 + 5 + 43 =  823;
%e A253915 6^4 + 6^3 + 6^2 + 6 + 43 = 1597;
%e A253915 7^4 + 7^3 + 7^2 + 7 + 43 = 2843;
%e A253915 8^4 + 8^3 + 8^2 + 8 + 43 = 4723;
%e A253915 all nine are primes, and
%e A253915 9^4 + 9^3 + 9^2 + 9 + 43 = 7423 = 13*571 is composite.
%e A253915 The next prime for p=43 appears for k=13, namely 30983.
%t A253915 Select[Prime[Range[118*10^5]],AllTrue[#+{0,4,30,120,340,780,1554,2800,4680},PrimeQ]&&CompositeQ[#+7380]&] (* _Harvey P. Dale_, Sep 10 2021 *)
%o A253915 (PARI) forprime(p=1, 1e10, if(isprime(p+4)&& isprime(p+30)&& isprime(p+120)&& isprime(p+340)&& isprime(p+780)&& isprime(p+1554)&& isprime(p+2800)&& isprime(p+4680) && !isprime(p+7380), print1(p,", ")))
%Y A253915 Cf. A027445, A144051, A187057, A187058, A187060, A190800, A191456, A191457, A191458, A247949, A247966, A248206.
%K A253915 nonn
%O A253915 1,1
%A A253915 _K. D. Bajpai_, Jan 18 2015
%E A253915 Edited by _Wolfdieter Lang_, Feb 20 2015
%E A253915 Corrected and extended by _Harvey P. Dale_, Sep 10 2021