A128033 - OEIS

%I #8 Nov 29 2020 01:03:34

%S 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,

%T 0,3,2,0,2,401,0,3,2,0,5,5,0,3,2,0

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

%C All positive terms are primes.

%C 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}.

%C a(49) > 10000. - _Jinyuan Wang_, Nov 28 2020

%F a(3*n) = 0.

%o (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

%Y 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.

%K nonn,hard,more

%O 0,2

%A _Alexander Adamchuk_, Feb 11 2007