A207838 Numbers k such that 5*k^4 + 1 is prime.

6, 12, 114, 120, 324, 336, 390, 420, 498, 504, 540, 672, 756, 768, 840, 852, 876, 1014, 1062, 1092, 1122, 1170, 1188, 1248, 1266, 1314, 1344, 1398, 1440, 1470, 1524, 1758, 1770, 1818, 1860, 1968, 2028, 2046, 2088, 2184, 2190, 2232, 2262, 2268, 2304, 2382, 2430

Offset: 1

Author

Bruno Berselli, Feb 21 2012

Keywords

• nonn
• easy

Comments

All terms are multiples of 6.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A207837 (primes of the form 5*k^4+1).

Cf. A005097, A111051, A115104.

Programs

Magma

[6*n: n in [1..406] | IsPrime(6480*n^4+1)];

Mathematica

Select[Range[2440], PrimeQ[5 #^4 + 1] &] (* by definition *)

PARI

for(n=1, 406, r=6480*n^4+1; if(isprime(r), print1(6*n", ")));

Formula

a(n) = ((A207837(n) - 1)/5)^1/4. - Paul F. Marrero Romero, Dec 07 2023