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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

a(-n) = A128049(n), where A128049(n) = {0,2,3,2,2,3,0,3,2,2,3,2,0,2,3,0,3,2,0,2,37,...} Least number k>0 such that (3^k - (3-n)^k)/n is prime, or 0 if no such prime exists. a(3n) = 0. 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(123)-a(127) = {0,3,2,0,3}. a(129)-a(147) = {0,3,2,0,2,41,0,19,3,0,3,3,0,5,2,0,2,13,0}. a(149)-a(162) = {7,0,2,3,0,439,3,0,2,359,0,3,2,0}. a(n)>541 = Prime[100] for n = {49,68,122,128,148,...}.

LINKS

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

CROSSREFS

Cf. A128049 = Least number k>0 such that (3^k - (3-n)^k)/n is prime, or 0 if no such prime exists. Cf. A028491 = numbers n such that (3^n - 1)/2 is prime. Cf. A057468 = numbers n such that 3^n - 2^n is prime. Cf. A059801 = numbers n such that 4^n - 3^n is prime. Cf. A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Sequence in context: A027737 A063970 A130769 * A090954 A089778 A088253

Adjacent sequences:  A128030 A128031 A128032 * A128034 A128035 A128036

KEYWORD

hard,more,nonn

AUTHOR

Alexander Adamchuk, Feb 11 2007

STATUS

approved

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Last modified July 16 23:49 EDT 2019. Contains 325092 sequences. (Running on oeis4.)