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

%I A335124 #9 Sep 22 2023 08:57:20
%S A335124 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,
%T A335124 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,
%U A335124 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
%N A335124 Minimum part of the n-th reversed integer partition in Abramowitz-Stegun order; a(0) = 0.
%C A335124 The ordering of reversed partitions is first by sum, then by length, and finally lexicographically. The version for non-reversed partitions is A335123.
%H A335124 OEIS Wiki, <a href="http://oeis.org/wiki/Orderings of partitions">Orderings of partitions</a>
%H A335124 Wikiversity, <a href="https://en.wikiversity.org/wiki/Lexicographic_and_colexicographic_order">Lexicographic and colexicographic order</a>
%F A335124 a(n) = A055396(A185974(n)).
%e A335124 Triangle begins:
%e A335124   0
%e A335124   1
%e A335124   2 1
%e A335124   3 1 1
%e A335124   4 1 2 1 1
%e A335124   5 1 2 1 1 1 1
%e A335124   6 1 2 3 1 1 2 1 1 1 1
%e A335124   7 1 2 3 1 1 1 2 1 1 1 1 1 1 1
%e A335124   8 1 2 3 4 1 1 1 2 2 1 1 1 1 2 1 1 1 1 1 1 1
%t A335124 Table[If[n==0,{0},Min/@Sort[Reverse/@IntegerPartitions[n]]],{n,0,8}]
%Y A335124 Row lengths are A000041.
%Y A335124 Partition minima of A036036.
%Y A335124 The length of the same partition is A036043.
%Y A335124 The maximum of the same partition is A049085.
%Y A335124 The number of distinct parts in the same partition is A103921.
%Y A335124 The Heinz number of the same partition is A185974.
%Y A335124 The version for non-reversed partitions is A335123.
%Y A335124 Lexicographically ordered reversed partitions are A026791.
%Y A335124 Partitions in (sum/length/colex) order are A036037.
%Y A335124 Partitions in opposite Abramowitz-Stegun (sum/length/revlex) order are A334439.
%Y A335124 Cf. A124734, A193073, A334301, A334302, A334433, A334435.
%K A335124 nonn,tabf
%O A335124 0,3
%A A335124 _Gus Wiseman_, May 24 2020