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

0,3

Links

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

OEIS Wiki, Orderings of partitions

Wikiversity, Lexicographic and colexicographic order

Formula

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

Example

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

Mathematica

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

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.

Sequence in context: A209235 A062534 A143349 * A182715 A088425 A141294

Adjacent sequences: A335120 A335121 A335122 * A335124 A335125 A335126

Keyword

nonn,tabf

Author

Gus Wiseman, May 24 2020

Status

approved