A239475 Least number k such that k^n + n and k^n - n are both prime, or 0 if no such number exists.

4, 3, 2, 0, 42, 175, 66, 3, 2, 4983, 1770, 55055, 28686, 18765, 8456, 0, 594, 128345, 136080, 81, 92, 1163409, 18810, 10415, 11754, 3855, 0, 86043, 38880, 17639, 26088, 37293, 5540, 612015, 6876, 0, 44220, 130425, 110, 9292527, 1004850, 1812149, 442404, 1007445, 570658

Offset

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..45.

Formula

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

Example

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.

Prog

(Python)
import sympy
from sympy import isprime
def TwoBoth(x):
..for k in range(1, 10**7):
....if isprime(k**x+x) and isprime(k**x-x):
......return k
x = 1
while x < 100:
..if TwoBoth(x) != None:
....print(TwoBoth(x))
..else:
....print(0)
..x += 1
(PARI) a(n)=for(k=1, 10^7, if(ispseudoprime(k^n-n)&&ispseudoprime(k^n+n), return(k)))
n=1; while(n<100, print1(a(n), ", "); n++)

Crossrefs

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

Sequence in context: A373750 A350493 A327351 * A100802 A022960 A023446

Adjacent sequences: A239472 A239473 A239474 * A239476 A239477 A239478

Keyword

nonn

Author

Derek Orr, Mar 20 2014

Status

approved