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

7, 43, 79, 457, 877, 967, 1093, 2437, 2683, 3187, 5077, 5923, 7933, 8233, 11923, 12889, 15787, 17389, 19993, 31543, 41113, 41617, 42457, 71359, 77863, 80683, 91393, 101719, 102643, 105967, 107347, 120163, 129733, 137593, 151783, 170263, 175723, 197569, 210127

Offset: 1

Author

K. D. Bajpai, Jan 11 2015

Keywords

• nonn

Comments

All terms == 1 mod 6. - Robert Israel, Jan 11 2015

Examples

			a(1) = 7:
0^4 + 0^3 + 0^2 + 0 + 7 = 7;
1^4 + 1^3 + 1^2 + 1 + 7 = 11;
2^4 + 2^3 + 2^2 + 2 + 7 = 37;
3^4 + 3^3 + 3^2 + 3 + 7 = 127;
4^4 + 4^3 + 4^2 + 4 + 7 = 347;
5^4 + 5^3 + 5^2 + 5 + 7 = 787;
all six are primes.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..6730

Crossrefs

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

Programs

Maple

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

Mathematica

Select[f=k^4 + k^3 + k^2 + k; k = {0, 1, 2, 3, 4, 5}; Prime[Range[2000000]], And @@ PrimeQ[#+f] &]
Select[Prime[Range[20000]],AllTrue[#+{4,30,120,340,780},PrimeQ]&] (* Harvey P. Dale, Dec 24 2023 *)

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,", ")))