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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,hard,more
AUTHOR
Alexander Adamchuk, Feb 11 2007
STATUS
approved

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Last modified April 17 17:01 EDT 2024. Contains 371765 sequences. (Running on oeis4.)