

A113914


(1,2,3) Jasinskilike positive power sequence.


1



1, 5, 13, 29, 61, 131, 271, 569, 1381, 2789, 5581, 11171, 22369, 44741, 89491, 185543, 373273, 766229, 1532701, 3065411, 6130849, 12261701, 24700549, 49401101, 98802211, 202387391, 409557751, 819116231, 1638232471, 3276464969
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OFFSET

1,2


COMMENTS

In general, the (b,c,d) Jasinskilike positive power sequence is defined as follows: a(1) = b, a(n+1) = the least prime p such that p = c*a(n) + d^k for positive integer k. The (b,c,d) Jasinskilike nonnegative power sequence is defined: a(1) = b, a(n+1) = the least prime p such that p = c*a(n) + d^k for integer k. In this notation, A113824 is the (1,2,2) Jasinskilike nonnegative power sequence. The first differences of such sequences are powers of d, with no closedform known upper bound.


LINKS

Table of n, a(n) for n=1..30.


FORMULA

a(1) = 1, a(n+1) = the least prime p such that p = 2*a(n) + 3^k for integer k>0.


EXAMPLE

a(1) = 1 by definition.
a(2) = 2*1 + 3^1 = 5.
a(3) = 2*5 + 3^1 = 13.
a(4) = 2*13 + 3^1 = 29.
a(5) = 2*29 + 3^1 = 61.
a(6) = 2*61 + 3^2 = 271.
a(7) = 2*271 + 3^2 = 569.
a(32) = 2*6553461379 + 3^49 = 239299329230630636512841. Here 49 is a record value for the exponent.


CROSSREFS

Cf. A073924, A080355, A080567, A099969, A099970, A099971, A099972, A113824.
Sequence in context: A120274 A036982 A029580 * A050415 A099970 A073857
Adjacent sequences: A113911 A113912 A113913 * A113915 A113916 A113917


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Jan 29 2006


STATUS

approved



