

A113787


Number of iterations of signature function required to get to [1] from partitions in Abramowitz and Stegun order.


3



0, 1, 2, 1, 3, 2, 1, 3, 2, 4, 2, 1, 3, 3, 4, 4, 4, 2, 1, 3, 3, 2, 4, 3, 2, 4, 3, 4, 2, 1, 3, 3, 3, 4, 3, 4, 4, 4, 5, 4, 4, 4, 4, 2, 1, 3, 3, 3, 2, 4, 3, 3, 4, 4, 4, 5, 3, 5, 2, 4, 5, 4, 4, 4, 4, 2, 1, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3, 2, 4, 5, 5, 5, 5, 4, 4, 5, 4, 5, 4, 4, 5, 3, 4, 4, 4, 2
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OFFSET

1,3


COMMENTS

The signature function takes a partition to the partition consisting of its repetition factors.


LINKS

Robert Price, Table of n, a(n) for n = 1..9295 (first 25 rows).
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].


EXAMPLE

Partition 5 in A&S order is [1,2]. Applying the signature function to this repeatedly gives [1,2] > [1^2] > [2] > [1], so a(5)=3.


MATHEMATICA

sig[x_] := Length@NestWhileList[Last@Transpose@Tally@# &, x, # != {1} &, 1]  1;
Table[sig /@ Sort[Reverse /@ IntegerPartitions[n]], {n, 9}] // Flatten (* Robert Price, Jun 12 2020 *)


CROSSREFS

Cf. A115621, A115624, Sequence of first partitions with a(m)=n is A012257, with initial rows {1} and {2} in prepended. See A036036 for A&S partitions.
Sequence in context: A256440 A088370 A328719 * A115624 A076291 A275015
Adjacent sequences: A113784 A113785 A113786 * A113788 A113789 A113790


KEYWORD

easy,nonn


AUTHOR

Franklin T. AdamsWatters, Jan 20 2006


STATUS

approved



