A239475 - OEIS

%I #16 Jul 18 2014 22:30:04

%S 4,3,2,0,42,175,66,3,2,4983,1770,55055,28686,18765,8456,0,594,128345,

%T 136080,81,92,1163409,18810,10415,11754,3855,0,86043,38880,17639,

%U 26088,37293,5540,612015,6876,0,44220,130425,110,9292527,1004850,1812149,442404,1007445,570658

%N Least number k such that k^n + n and k^n - n are both prime, or 0 if no such number exists.

%C a(n) = 0 iff n is of the form (pk)^p for some k and some prime p (See A097764).

%C gcd(n,a(n)) = 1 for all a(n) > 0.

%F a(A097764(n)) = 0 for all n.

%e 1^1 +/- 1 = 2 and 0 are not both primes. 2^1 +/- 1 = 3 and 1 are not both primes. 3^1 +/- 1 = 4 and 2 are not both primes. 4^1 +/- 1 = 5 and 3 are both primes. Thus a(1) = 4.

%o (Python)

%o import sympy

%o from sympy import isprime

%o def TwoBoth(x):

%o ..for k in range(1,10**7):

%o ....if isprime(k**x+x) and isprime(k**x-x):

%o ......return k

%o x = 1

%o while x < 100:

%o ..if TwoBoth(x) != None:

%o ....print(TwoBoth(x))

%o ..else:

%o ....print(0)

%o ..x += 1

%o (PARI) a(n)=for(k=1,10^7,if(ispseudoprime(k^n-n)&&ispseudoprime(k^n+n),return(k)))

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

%Y Cf. A072883, A028870, A153974, A239413, A239414, A239415, A239416, A239417, A239418, A239474.

%K nonn

%O 1,1

%A _Derek Orr_, Mar 20 2014