A242552 Least number k such that n^4 + k^4 is prime.

1, 1, 2, 1, 2, 1, 2, 3, 2, 7, 2, 13, 4, 5, 8, 1, 2, 5, 2, 1, 10, 15, 2, 1, 6, 3, 2, 1, 12, 7, 12, 5, 14, 1, 6, 7, 2, 3, 14, 9, 2, 5, 10, 21, 2, 1, 4, 1, 2, 7, 2, 11, 6, 1, 14, 1, 2, 7, 2, 11, 2, 11, 8, 23, 16, 29, 12, 3, 10, 27, 2, 5, 8, 1, 8, 3, 20, 17, 2, 1, 10, 1, 10

Offset

1,3

Comments

If a(n) = 1, then n is in A000068.

Links

Table of n, a(n) for n=1..83.

Example

8^4+1^4 = 4097 is not prime. 8^4+2^4 = 4112 is not prime. 8^4+3^4 = 4177 is prime. Thus, a(8) = 3.

Mathematica

Table[Module[{c=n^4, k=1}, While[CompositeQ[c+ k^4], k++]; k], {n, 90}] (* Harvey P. Dale, Jun 03 2026 *)

Prog

(Python)
import sympy
from sympy import isprime
def a(n):
  for k in range(10**4):
    if isprime(n**4+k**4):
      return k
n = 1
while n < 100:
  print(a(n))
  n += 1
(PARI) a(n)=for(k=1, oo, if(ispseudoprime(n^4+k^4), return(k)));

Crossrefs

Cf. A069003, A000068.

Sequence in context: A373461 A257806 A035391 * A249717 A249718 A244518

Adjacent sequences: A242549 A242550 A242551 * A242553 A242554 A242555

Keyword

nonn,changed

Author

Derek Orr, May 17 2014

Status

approved