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
Keywords
Examples
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.
Crossrefs
Programs
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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++)
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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
Formula
a(A097764(n)) = 0 for all n.
Comments