A128049 -id:A128049 - cp's OEIS frontend

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A128033 Least number k>0 such that ((n+3)^k - 3^k)/n is prime, or 0 if no such prime exists.

Original entry on oeis.org

0, 2, 13, 0, 3, 2, 0, 2, 3, 0, 7, 2, 0, 2, 3, 0, 73, 2, 0, 5, 3, 0, 3, 2, 0, 2, 3, 0, 3, 3, 0, 2, 5, 0, 3, 2, 0, 2, 401, 0, 3, 2, 0, 5, 5, 0, 3, 2, 0

Offset: 0

Alexander Adamchuk, Feb 11 2007

All positive terms are primes.
a(50)-a(67) = {7, 0, 79, 2, 0, 2, 109, 0, 5, 5, 0, 2, 5, 0, 131, 2, 0, 2}. a(69)-a(121) = {0, 3, 19, 0, 2, 5, 0, 11, 2, 0, 13, 7, 0, 3, 2, 0, 3, 11, 0, 3, 19, 0, 2, 3, 0, 11, 2, 0, 2, 3, 0, 17, 2, 0, 2, 3, 0, 5, 2, 0, 3, 31, 0, 17, 5, 0, 47, 31, 0, 3, 3, 0, 2}.
a(49) > 10000. - Jinyuan Wang, Nov 28 2020

Cf. A128049 (least number k>0 such that abs((3^k - (3-n)^k)/n) is prime), A028491, A121877, A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

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

a(3*n) = 0.

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