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

43, 457, 967, 1093, 5923, 8233, 11923, 15787, 41113, 80683, 151783, 210127, 213943, 294919, 392737, 430879, 495559, 524827, 537007, 572629, 584557, 711727, 730633, 731593, 1097293, 1123879, 1138363, 1149163, 1396207, 1601503, 1739557, 1824139, 2198407, 2223853

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..1405

Example

a(1) = 43:
0^4 + 0^3 + 0^2 + 0 + 43 = 43;
1^4 + 1^3 + 1^2 + 1 + 43 = 47;
2^4 + 2^3 + 2^2 + 2 + 43 = 73;
3^4 + 3^3 + 3^2 + 3 + 43 = 163;
4^4 + 4^3 + 4^2 + 4 + 43 = 383;
5^4 + 5^3 + 5^2 + 5 + 43 = 823;
6^4 + 6^3 + 6^2 + 6 + 43 = 1597;
all seven are primes.

Mathematica

Select[f=k^4 + k^3 + k^2 + k; k = {0, 1, 2, 3, 4, 5, 6}; Prime[Range[2000000]], And @@ PrimeQ[#+f] &]
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 *)

Prog

(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, ", ")))

Crossrefs

Cf. A144051, A187057, A187058, A187060, A190800, A191456, A191457, A191458.

Sequence in context: A093673 A244769 A239268 * A248206 A140849 A188133

Adjacent sequences: A247963 A247964 A247965 * A247967 A247968 A247969

Keyword

nonn

Author

K. D. Bajpai, Jan 11 2015

Status

approved