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.
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
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jan 29 2006
STATUS
approved