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

%I A242553 #12 Dec 26 2024 18:58:21
%S A242553 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,
%T A242553 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,
%U A242553 2,11,10,3,4,49,6,71,22,15,14,47,30,9,2,19,6,19,6,5,28,13,2
%N A242553 Least number k such that n^8 + k^8 is prime.
%C A242553 If a(n) = 1, then n is in A006314.
%e A242553 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.
%t A242553 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 *)
%o A242553 (Python)
%o A242553 import sympy
%o A242553 from sympy import isprime
%o A242553 def a(n):
%o A242553   for k in range(10**4):
%o A242553     if isprime(n**8+k**8):
%o A242553       return k
%o A242553 n = 1
%o A242553 while n < 100:
%o A242553   print(a(n))
%o A242553   n += 1
%o A242553 (PARI) a(n)=for(k=1,oo,if(ispseudoprime(n^8+k^8),return(k)));
%Y A242553 Cf. A069003, A006314.
%K A242553 nonn
%O A242553 1,3
%A A242553 _Derek Orr_, May 17 2014