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

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

0,2

Comments

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

Links

Table of n, a(n) for n=0..48.

Formula

a(3*n) = 0.

Prog

(PARI) 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

Crossrefs

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.

Sequence in context: A063970 A309864 A130769 * A090954 A089778 A088253

Adjacent sequences: A128030 A128031 A128032 * A128034 A128035 A128036

Keyword

nonn,hard,more

Author

Alexander Adamchuk, Feb 11 2007

Status

approved