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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 (list; graph; refs; listen; history; text; internal format)
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 n-th 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(n-i+1)) is semiprime}. a(n) = min {n>0: SUM[from i = 1 to n] (a(i))^(a(n-i+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

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Last modified October 15 05:56 EDT 2018. Contains 316202 sequences. (Running on oeis4.)