A128049 Least number k>0 such that abs((3^k - (3-n)^k)/n) is prime, or 0 if no such prime exists.

0, 2, 3, 2, 2, 3, 0, 3, 2, 2, 3, 2, 0, 2, 3, 0, 3, 2, 0, 2, 37, 0, 3, 2, 0, 2, 1153, 0, 83, 2, 0, 3, 11, 0, 3, 2, 0, 2, 3, 0, 557, 19, 0, 2, 3, 0, 7, 2, 0, 2, 631, 0, 5, 2, 0, 3, 3, 0, 239, 2, 0, 5, 3, 0, 3, 2, 0, 2, 317, 0, 3, 103, 0, 2, 7, 0, 3, 2, 0, 2, 43

Offset: 0

Author

Alexander Adamchuk, Feb 12 2007

Keywords

• nonn

Comments

a(-n) = A128033(n).

a(3*n) = 0 except a(3) = a(9) = 2.

All positive terms are primes.

Links

• Jinyuan Wang, Table of n, a(n) for n = 0..222

Crossrefs

Cf. A128033 (least number k>0 such that ((n+3)^k - 3^k)/n is prime), A028491 (numbers n such that (3^n - 1)/2 is prime).

Cf. A111010, A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Programs

PARI

a(n) = my(p=3); if(isprime(abs(n-6)), 2, if(n%3, while(!ispseudoprime((3^p-(3-n)^p)/n), p=nextprime(p+1)); p, 0)); \\ Jinyuan Wang, Nov 28 2020

Extensions

Name changed by Jinyuan Wang, Nov 28 2020