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Least number k such that k^64 + n^64 is prime.
1

%I #12 Dec 26 2024 19:53:33

%S 1,37,32,39,118,13,16,11,154,41,8,29,6,17,64,7,14,107,66,63,58,87,38,

%T 397,282,69,32,129,12,67,210,3,200,227,82,55,2,7,4,541,10,103,64,167,

%U 286,71,60,593,6,459,14,3,2,91,4,81,98,21,164,47,36,51,10,15,84,19,30

%N Least number k such that k^64 + n^64 is prime.

%C If a(n) = 1, then n is in A006316.

%t lnk[n_]:=Module[{c=n^64,k=1},While[!PrimeQ[c+k^64],k++];k]; Array[lnk,70] (* _Harvey P. Dale_, Oct 21 2017 *)

%o (Python)

%o import sympy

%o from sympy import isprime

%o def a(n):

%o for k in range(10**4):

%o if isprime(n**64+k**64):

%o return k

%o n = 1

%o while n < 100:

%o print(a(n))

%o n += 1

%o (PARI) a(n)=for(k=1,oo,if(ispseudoprime(n^64+k^64),return(k)));

%Y Cf. A069003, A006316.

%K nonn

%O 1,2

%A _Derek Orr_, May 17 2014