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%I #3 Mar 30 2012 18:40:34
%S 1,5,13,29,61,131,271,569,1381,2789,5581,11171,22369,44741,89491,
%T 185543,373273,766229,1532701,3065411,6130849,12261701,24700549,
%U 49401101,98802211,202387391,409557751,819116231,1638232471,3276464969
%N (1,2,3) Jasinski-like positive power sequence.
%C 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.
%F a(1) = 1, a(n+1) = the least prime p such that p = 2*a(n) + 3^k for integer k>0.
%e a(1) = 1 by definition.
%e a(2) = 2*1 + 3^1 = 5.
%e a(3) = 2*5 + 3^1 = 13.
%e a(4) = 2*13 + 3^1 = 29.
%e a(5) = 2*29 + 3^1 = 61.
%e a(6) = 2*61 + 3^2 = 271.
%e a(7) = 2*271 + 3^2 = 569.
%e a(32) = 2*6553461379 + 3^49 = 239299329230630636512841. Here 49 is a record value for the exponent.
%Y Cf. A073924, A080355, A080567, A099969, A099970, A099971, A099972, A113824.
%K easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Jan 29 2006
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