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

0,2

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

Prog

(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

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.

Sequence in context: A145390 A270026 A340703 * A104543 A054988 A143393

Adjacent sequences: A128046 A128047 A128048 * A128050 A128051 A128052

Keyword

nonn

Author

Alexander Adamchuk, Feb 12 2007

Extensions

Name changed by Jinyuan Wang, Nov 28 2020

Status

approved