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

Author

Gus Wiseman, May 24 2020

Keywords

• nonn
• tabf

Comments

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

Examples

			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
		

Links

• OEIS Wiki, Orderings of partitions
• Wikiversity, Lexicographic and colexicographic order

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.

Programs

Mathematica

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

Formula

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