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 A113320 Least integers so ascending descending base exponent transforms all prime. 8
 1, 1, 1, 2, 2, 4, 4, 4, 6, 2, 6, 4, 18, 6, 4, 20, 6, 30, 4, 40, 30, 8, 18, 16, 40, 128, 24, 40, 58, 194, 78, 84, 56, 56, 72, 112, 98, 300, 444, 54, 978, 1938, 120, 126, 6, 1750 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS This is the first sequence submitted as a solution to an "ascending descending base exponent transform inverse problem" where the sequence is iteratively defined such that the transform meets a constraint. The sequence is infinite, but it is hard to characterize the asymptotic cost of adding an n-th term. A003101 is the ascending descending base exponent transform of natural numbers A000027. The ascending descending base exponent transform applied to the Fibonacci numbers is A113122; applied to the tribonacci numbers is A113153; applied to the Lucas numbers is A113154. LINKS FORMULA a(1) = 1. For n>1: a(n) = min {n>0: SUM[from i = 1 to n] (a(i))^(a(n-i+1)) is prime}. EXAMPLE a(1) = 1 by definition. a(2) = 1 because 1 is the min such that 1^a(2) + a(2)^1 is prime (p=2). a(3) = 1 because 1 is the min such that 1^a(3) + 1^1 + a(3)^1 is prime (p=5). a(4) = 2 because 2 is the min such that 1^a(4) + 1^1 + 3^1 + a(4)^1 is prime (p=7). MATHEMATICA inve[w_] := Total[w^Reverse[w]]; a[1] = 1; a[n_] := a[n] = Block[{k = 0}, While[! PrimeQ[ inve@ Append[Array[a, n-1], ++k]]]; k]; Array[a, 46] (* Giovanni Resta, Jun 13 2016 *) CROSSREFS Cf. A000040, A005408, A113122, A113153, A113154. Sequence in context: A157887 A292264 A265263 * A085237 A279891 A110870 Adjacent sequences:  A113317 A113318 A113319 * A113321 A113322 A113323 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Jan 07 2006 EXTENSIONS Corrected and extended by Giovanni Resta, Jun 13 2016 STATUS approved

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Last modified October 22 04:25 EDT 2019. Contains 328315 sequences. (Running on oeis4.)