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A113914 (1,2,3) Jasinski-like 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 3 07:58 EST 2022. Contains 358515 sequences. (Running on oeis4.)