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

%I A335123 #12 Sep 22 2023 08:58:32
%S A335123 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,
%T A335123 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,
%U A335123 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
%N A335123 Minimum part of the n-th integer partition in Abramowitz-Stegun order (sum/length/lex); a(0) = 0.
%H A335123 OEIS Wiki, <a href="http://oeis.org/wiki/Orderings of partitions">Orderings of partitions</a>
%H A335123 Wikiversity, <a href="https://en.wikiversity.org/wiki/Lexicographic_and_colexicographic_order">Lexicographic and colexicographic order</a>
%F A335123 a(n) = A055396(A334433(n)).
%e A335123 Triangle begins:
%e A335123   0
%e A335123   1
%e A335123   2 1
%e A335123   3 1 1
%e A335123   4 2 1 1 1
%e A335123   5 2 1 1 1 1 1
%e A335123   6 3 2 1 2 1 1 1 1 1 1
%e A335123   7 3 2 1 2 1 1 1 1 1 1 1 1 1 1
%e A335123   8 4 3 2 1 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
%t A335123 Table[If[n==0,{0},Min/@Sort[IntegerPartitions[n]]],{n,0,8}]
%Y A335123 Row lengths are A000041.
%Y A335123 Partition minima of A334301.
%Y A335123 The length of the same partition is A036043.
%Y A335123 The Heinz number of the same partition is A334433.
%Y A335123 The number of distinct parts in the same partition is A334440.
%Y A335123 The maximum of the same partition is A334441.
%Y A335123 The version for reversed partitions is A335124.
%Y A335123 Reversed partitions in Abramowitz-Stegun (sum/length/lex) order are A036036.
%Y A335123 Partitions in (sum/length/revlex) order are A334439.
%Y A335123 Cf. A026791, A049085, A103921, A124734, A185974, A193073, A334302, A334433.
%K A335123 nonn,tabf
%O A335123 0,3
%A A335123 _Gus Wiseman_, May 24 2020