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

%I #9 Jul 12 2014 22:44:04

%S 102,37,32,39,118,13,16,11,154,41,94,29,158,17,64,291,70,107,66,63,58,

%T 87,38,397,282,69,32,129,142,67,210,87,200,227,82,55,70,137,388,541,

%U 140,103,64,167,286,71,60,593,262,459,62,69,92,91,128,81,98,149,164,107,192,103

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

%C a(n) = n+1 iff n is in A174157.

%H Jens Kruse Andersen, <a href="/A244949/b244949.txt">Table of n, a(n) for n = 1..10000</a>

%e 8^64 + 11^64 = 4457915690803004131256192897205630962697827851093882159977969339137 is prime. Since 8^64 + 10^64 and 8^64 + 9^64 are both composite, a(8) = 11.

%o (Python)

%o import sympy

%o from sympy import isprime

%o def a(n):

%o ..for k in range(n+1,10**4):

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

%o ......return k

%o n = 1

%o while n < 100:

%o ..print(a(n),end=', ')

%o ..n += 1

%o (PARI) a(n)=for(k=n+1,10^4,if(isprime(k^64+n^64),return(k)))

%o n=1;while(n<100,print1(a(n),", ");n++)

%Y Cf. A158979, A089489, A242556.

%K nonn

%O 1,1

%A _Derek Orr_, Jul 08 2014