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

43, 457, 967, 11923, 15787, 41113, 213943, 294919, 392737, 430879, 524827, 572629, 730633, 1097293, 1149163, 2349313, 2738779, 3316147, 3666007, 5248153, 5396617, 5477089, 7960009, 9949627, 10048117, 11260237, 11613289, 15281023, 16153279, 17250367, 18733807

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..511

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;
7^4 + 7^3 + 7^2 + 7 + 43 = 2843;
all eight are primes.

Mathematica

Select[f=k^4+k^3+k^2+k; k={0, 1, 2, 3, 4, 5, 6, 7}; Prime[Range[2000000]], And @@ PrimeQ[#+f] &]
Select[Prime[Range[12*10^5]], AllTrue[#+{4, 30, 120, 340, 780, 1554, 2800}, PrimeQ]&] (* Harvey P. Dale, Apr 24 2022 *)

Prog

(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, ", ")))

Crossrefs

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

Sequence in context: A244769 A239268 A247966 * A140849 A188133 A194784

Adjacent sequences: A248203 A248204 A248205 * A248207 A248208 A248209

Keyword

nonn

Author

K. D. Bajpai, Jan 11 2015

Status

approved