A335123 Minimum part of the n-th integer partition in Abramowitz-Stegun order (sum/length/lex); a(0) = 0.

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

Offset: 0

Author

Gus Wiseman, May 24 2020

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  0
  1
  2 1
  3 1 1
  4 2 1 1 1
  5 2 1 1 1 1 1
  6 3 2 1 2 1 1 1 1 1 1
  7 3 2 1 2 1 1 1 1 1 1 1 1 1 1
  8 4 3 2 1 2 2 1 1 1 2 1 1 1 1 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 A334301.

The length of the same partition is A036043.

The Heinz number of the same partition is A334433.

The number of distinct parts in the same partition is A334440.

The maximum of the same partition is A334441.

The version for reversed partitions is A335124.

Reversed partitions in Abramowitz-Stegun (sum/length/lex) order are A036036.

Partitions in (sum/length/revlex) order are A334439.

Cf. A026791, A049085, A103921, A124734, A185974, A193073, A334302, A334433.

Programs

Mathematica

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

Formula

a(n) = A055396(A334433(n)).