

A113475


Least integers so ascending descending base exponent transforms all semiprime.


1



1, 3, 5, 2, 4, 2, 2, 4, 2, 4, 3, 2, 3, 4, 2, 2, 1, 1, 2, 1, 5, 1, 7, 1, 5, 4, 2, 2, 3, 3, 2, 11, 5, 10, 4, 2, 2, 6, 14, 4, 6, 2, 3, 9, 14, 10, 3, 3, 4, 2, 1, 5, 4, 16, 8, 9, 5, 8, 14, 6, 2, 2, 26, 8, 30, 4, 5, 1, 4, 2, 22, 36, 20, 2, 10, 2, 15, 3, 18, 6, 15
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OFFSET

1,2


COMMENTS

Semiprime analogy to A113320. The sequence is probably infinite, but it is hard to characterize the asymptotic cost of adding an nth term. The ascending descending base exponent transform of semiprimes is A113173.


LINKS

Table of n, a(n) for n=1..81.


FORMULA

a(1) = 1. For n>1: a(n) = min {n>0: SUM[from i = 1 to n] (a(i))^(a(ni+1)) is semiprime}. a(n) = min {n>0: SUM[from i = 1 to n] (a(i))^(a(ni+1)) in A001358}.


EXAMPLE

a(1) = 1 by definition.
a(2) = 3 because 3 is the min x such that 1^x + x^1 is semiprime,
i.e. 1^3 + 3^1 = 4 = 2*2.
a(3) = 5 because 1^5 + 3^3 + 5^1 = 33 = 3 * 11 is semiprime.
a(4) = 2 because 1^2 + 3^5 + 5^3 + 2^1 = 371 = 7 * 53.
a(5) = 4 because 1^4 + 3^2 + 5^5 + 2^3 + 4^1 = 3147 = 3 * 1049.
a(6) = 2 because 1^2 + 3^4 + 5^2 + 2^5 + 4^3 + 2^1 = 205 = 5 * 41.
a(7) = 2 because 1^2 + 3^2 + 5^4 + 2^2 + 4^5 + 2^3 + 2^1 = 1673 = 7 * 239.
a(8) = 4 because 1^4 + 3^2 + 5^2 + 2^4 + 4^2 + 2^5 + 2^3 + 4^1 = 111 = 3 * 37.


MATHEMATICA

semipQ[n_] := PrimeOmega[n] == 2; inve[w_] := Total[w^Reverse[w]]; a[1] = 1; a[n_] := a[n] = Block[{k = 0}, While[! semipQ[ inve@ Append[ Array[a, n  1], ++k]]]; k]; Array[a, 81] (* Giovanni Resta, Jun 13 2016 *)


CROSSREFS

Cf. A001358, A005408, A113122, A113153, A113154, A113336, A113320, A113271, A113258, A113257, A113231, A087316, A113208.
Sequence in context: A218888 A261597 A197331 * A182743 A222601 A104807
Adjacent sequences: A113472 A113473 A113474 * A113476 A113477 A113478


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Jan 08 2006


EXTENSIONS

Corrected and extended by Giovanni Resta, Jun 13 2016


STATUS

approved



