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A248206 Primes p such that the polynomial k^4 + k^3 + k^2 + k + p yields only primes for k = 0...7.

%I A248206 #13 Apr 24 2022 13:36:00
%S A248206 43,457,967,11923,15787,41113,213943,294919,392737,430879,524827,
%T A248206 572629,730633,1097293,1149163,2349313,2738779,3316147,3666007,
%U A248206 5248153,5396617,5477089,7960009,9949627,10048117,11260237,11613289,15281023,16153279,17250367,18733807
%N A248206 Primes p such that the polynomial k^4 + k^3 + k^2 + k + p yields only primes for k = 0...7.
%H A248206 K. D. Bajpai, <a href="/A248206/b248206.txt">Table of n, a(n) for n = 1..511</a>
%e A248206 a(1) = 43:
%e A248206 0^4 + 0^3 + 0^2 + 0 + 43 = 43;
%e A248206 1^4 + 1^3 + 1^2 + 1 + 43 = 47;
%e A248206 2^4 + 2^3 + 2^2 + 2 + 43 = 73;
%e A248206 3^4 + 3^3 + 3^2 + 3 + 43 = 163;
%e A248206 4^4 + 4^3 + 4^2 + 4 + 43 = 383;
%e A248206 5^4 + 5^3 + 5^2 + 5 + 43 = 823;
%e A248206 6^4 + 6^3 + 6^2 + 6 + 43 = 1597;
%e A248206 7^4 + 7^3 + 7^2 + 7 + 43 = 2843;
%e A248206 all eight are primes.
%t A248206 Select[f=k^4+k^3+k^2+k; k={0,1,2,3,4,5,6,7}; Prime[Range[2000000]], And @@ PrimeQ[#+f] &]
%t A248206 Select[Prime[Range[12*10^5]],AllTrue[#+{4,30,120,340,780,1554,2800},PrimeQ]&] (* _Harvey P. Dale_, Apr 24 2022 *)
%o A248206 (PARI) forprime(p=1, 1e8, if( isprime(p+0)& isprime(p+4)& isprime(p+30)& isprime(p+120)& isprime(p+340)& isprime(p+780)&  isprime(p+1554)& isprime(p+2800), print1(p,", ")))
%Y A248206 Cf. A144051, A187057, A187058, A187060, A190800, A191456, A191457, A191458.
%K A248206 nonn
%O A248206 1,1
%A A248206 _K. D. Bajpai_, Jan 11 2015