

A115624


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


3



0, 1, 2, 1, 3, 2, 1, 3, 2, 4, 2, 1, 3, 3, 4, 4, 4, 2, 1, 3, 3, 4, 2, 3, 4, 2, 3, 4, 2, 1, 3, 3, 4, 3, 3, 4, 4, 4, 5, 4, 4, 4, 4, 2, 1, 3, 3, 4, 3, 3, 4, 2, 3, 4, 5, 4, 4, 3, 5, 5, 4, 2, 4, 4, 4, 2, 1, 3, 3, 4, 3, 3, 4, 3, 3, 4, 5, 4, 4, 3, 5, 5, 5, 4, 2, 5, 4, 4, 5, 5, 4, 4, 3, 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).


EXAMPLE

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


MATHEMATICA

sig[x_] := Length@NestWhileList[Last@Transpose@Tally@# &, x, # != {1} &, 1]  1;
Table[sig /@ IntegerPartitions[n], {n, 8}] // Flatten (* Robert Price, Jun 12 2020 *)


CROSSREFS

Cf. A115621, A113787, Sequence of first partitions with a(m)=n is A012257, with initial rows {1} and {2} in prepended. See A080577 for Mathematica partition order.
Sequence in context: A088370 A328719 A113787 * A076291 A275015 A211189
Adjacent sequences: A115621 A115622 A115623 * A115625 A115626 A115627


KEYWORD

easy,nonn


AUTHOR

Franklin T. AdamsWatters, Jan 25 2006


STATUS

approved



