A113914 (1,2,3) Jasinski-like positive power sequence.

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

Offset

1,2

Comments

In general, the (b,c,d) Jasinski-like 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) Jasinski-like 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) Jasinski-like nonnegative power sequence. The first differences of such sequences are powers of d, with no closed-form 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: A036982 A029580 A344920 * A050415 A099970 A073857

Adjacent sequences: A113911 A113912 A113913 * A113915 A113916 A113917

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 29 2006

Status

approved