login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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(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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 09:28 EDT 2018. Contains 316339 sequences. (Running on oeis4.)