This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A113914 #3 Mar 30 2012 18:40:34 %S A113914 1,5,13,29,61,131,271,569,1381,2789,5581,11171,22369,44741,89491, %T A113914 185543,373273,766229,1532701,3065411,6130849,12261701,24700549, %U A113914 49401101,98802211,202387391,409557751,819116231,1638232471,3276464969 %N A113914 (1,2,3) Jasinski-like positive power sequence. %C A113914 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 A113914 a(1) = 1, a(n+1) = the least prime p such that p = 2*a(n) + 3^k for integer k>0. %e A113914 a(1) = 1 by definition. %e A113914 a(2) = 2*1 + 3^1 = 5. %e A113914 a(3) = 2*5 + 3^1 = 13. %e A113914 a(4) = 2*13 + 3^1 = 29. %e A113914 a(5) = 2*29 + 3^1 = 61. %e A113914 a(6) = 2*61 + 3^2 = 271. %e A113914 a(7) = 2*271 + 3^2 = 569. %e A113914 a(32) = 2*6553461379 + 3^49 = 239299329230630636512841. Here 49 is a record value for the exponent. %Y A113914 Cf. A073924, A080355, A080567, A099969, A099970, A099971, A099972, A113824. %K A113914 easy,nonn %O A113914 1,2 %A A113914 _Jonathan Vos Post_, Jan 29 2006