A115624 Number of iterations of signature function required to get to [1] from partitions in Mathematica order.

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

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 A370264

Adjacent sequences: A115621 A115622 A115623 * A115625 A115626 A115627

Keyword

easy,nonn

Author

Franklin T. Adams-Watters, Jan 25 2006

Status

approved