A242553 Least number k such that n^8 + k^8 is prime.

1, 1, 10, 1, 6, 5, 12, 13, 16, 3, 24, 7, 2, 3, 8, 9, 4, 17, 4, 7, 2, 3, 20, 7, 8, 19, 10, 3, 10, 19, 14, 17, 32, 11, 8, 25, 6, 25, 40, 7, 10, 43, 16, 5, 68, 7, 30, 5, 8, 19, 58, 17, 26, 17, 2, 11, 10, 3, 4, 49, 6, 71, 22, 15, 14, 47, 30, 9, 2, 19, 6, 19, 6, 5, 28, 13, 2

Offset

1,3

Comments

If a(n) = 1, then n is in A006314.

Links

Table of n, a(n) for n=1..77.

Example

10^8+1^8 = 100000001 is not prime. 10^8+2^8 = 100000256 is not prime. 10^8+3^8 = 100006561 is prime. Thus, a(10) = 3.

Mathematica

lnk[n_]:=Module[{c=n^8, k=1}, While[CompositeQ[c+k^8], k++]; k]; Array[lnk, 80] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 12 2020 *)

Prog

(Python)
import sympy
from sympy import isprime
def a(n):
  for k in range(10**4):
    if isprime(n**8+k**8):
      return k
n = 1
while n < 100:
  print(a(n))
  n += 1
(PARI) a(n)=for(k=1, oo, if(ispseudoprime(n^8+k^8), return(k)));

Crossrefs

Cf. A069003, A006314.

Sequence in context: A321097 A015810 A010183 * A113513 A092030 A014538

Adjacent sequences: A242550 A242551 A242552 * A242554 A242555 A242556

Keyword

nonn

Author

Derek Orr, May 17 2014

Status

approved