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A239475
Least number k such that k^n + n and k^n - n are both prime, or 0 if no such number exists.
0
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.
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++)
KEYWORD
nonn
AUTHOR
Derek Orr, Mar 20 2014
STATUS
approved