

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
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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 nth 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

Table of n, a(n) for n=1..46.


FORMULA

a(1) = 1. For n>1: a(n) = min {n>0: SUM[from i = 1 to n] (a(i))^(a(ni+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, n1], ++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



