A335124 Minimum part of the n-th reversed integer partition in Abramowitz-Stegun order; a(0) = 0.

0, 1, 2, 1, 3, 1, 1, 4, 1, 2, 1, 1, 5, 1, 2, 1, 1, 1, 1, 6, 1, 2, 3, 1, 1, 2, 1, 1, 1, 1, 7, 1, 2, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 8, 1, 2, 3, 4, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 9, 1, 2, 3, 4, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,3

Comments

The ordering of reversed partitions is first by sum, then by length, and finally lexicographically. The version for non-reversed partitions is A335123.

Links

Table of n, a(n) for n=0..96.

OEIS Wiki, Orderings of partitions

Wikiversity, Lexicographic and colexicographic order

Formula

a(n) = A055396(A185974(n)).

Example

Triangle begins:
  0
  1
  2 1
  3 1 1
  4 1 2 1 1
  5 1 2 1 1 1 1
  6 1 2 3 1 1 2 1 1 1 1
  7 1 2 3 1 1 1 2 1 1 1 1 1 1 1
  8 1 2 3 4 1 1 1 2 2 1 1 1 1 2 1 1 1 1 1 1 1

Mathematica

Table[If[n==0, {0}, Min/@Sort[Reverse/@IntegerPartitions[n]]], {n, 0, 8}]

Crossrefs

Row lengths are A000041.

Partition minima of A036036.

The length of the same partition is A036043.

The maximum of the same partition is A049085.

The number of distinct parts in the same partition is A103921.

The Heinz number of the same partition is A185974.

The version for non-reversed partitions is A335123.

Lexicographically ordered reversed partitions are A026791.

Partitions in (sum/length/colex) order are A036037.

Partitions in opposite Abramowitz-Stegun (sum/length/revlex) order are A334439.

Cf. A124734, A193073, A334301, A334302, A334433, A334435.

Sequence in context: A367849 A263646 A113924 * A367579 A262891 A178340

Adjacent sequences: A335121 A335122 A335123 * A335125 A335126 A335127

Keyword

nonn,tabf

Author

Gus Wiseman, May 24 2020

Status

approved