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A335279 Positions of first appearances in A124771 = number of distinct contiguous subsequences of compositions in standard order.

%I A335279 #7 Jun 04 2020 06:40:04
%S A335279 0,1,3,5,11,15,23,27,37,47,55,107,111,119,155,215,223,239,411,431,471,
%T A335279 479,495,549,631,943,951,959,991,1647,1887,1967,1983,2015,2543,2935,
%U A335279 3703,3807,3935,3967,4031,6639,6895,7407,7871,7903,8063,8127,10207,13279
%N A335279 Positions of first appearances in A124771 = number of distinct contiguous subsequences of compositions in standard order.
%e A335279 The sequence together with the corresponding compositions begins:
%e A335279      0: ()                215: (1,2,2,1,1,1)
%e A335279      1: (1)               223: (1,2,1,1,1,1,1)
%e A335279      3: (1,1)             239: (1,1,2,1,1,1,1)
%e A335279      5: (2,1)             411: (1,3,1,2,1,1)
%e A335279     11: (2,1,1)           431: (1,2,2,1,1,1,1)
%e A335279     15: (1,1,1,1)         471: (1,1,2,2,1,1,1)
%e A335279     23: (2,1,1,1)         479: (1,1,2,1,1,1,1,1)
%e A335279     27: (1,2,1,1)         495: (1,1,1,2,1,1,1,1)
%e A335279     37: (3,2,1)           549: (4,3,2,1)
%e A335279     47: (2,1,1,1,1)       631: (3,1,1,2,1,1,1)
%e A335279     55: (1,2,1,1,1)       943: (1,1,2,2,1,1,1,1)
%e A335279    107: (1,2,2,1,1)       951: (1,1,2,1,2,1,1,1)
%e A335279    111: (1,2,1,1,1,1)     959: (1,1,2,1,1,1,1,1,1)
%e A335279    119: (1,1,2,1,1,1)     991: (1,1,1,2,1,1,1,1,1)
%e A335279    155: (3,1,2,1,1)      1647: (1,3,1,2,1,1,1,1)
%e A335279 The subsequences for n = 0, 1, 3, 5, 11, 15, 23, 27 are the following (0 = empty partition):
%e A335279   0  0  0   0   0    0     0     0     0    0
%e A335279      1  1   1   1    1     1     1     1    1
%e A335279         11  2   2    11    2     2     2    2
%e A335279             21  11   111   11    11    3    11
%e A335279                 21   1111  21    12    21   21
%e A335279                 211        111   21    32   111
%e A335279                            211   121   321  211
%e A335279                            2111  211        1111
%e A335279                                  1211       2111
%e A335279                                             21111
%t A335279 stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t A335279 seq=Table[Length[Union[ReplaceList[stc[n],{___,s___,___}:>{s}]]],{n,0,1000}];
%t A335279 Table[Position[seq,i][[1,1]]-1,{i,First/@Gather[seq]}]
%Y A335279 Positions of first appearances in A124771.
%Y A335279 Compositions where every subinterval has a different sum are A333222.
%Y A335279 Knapsack compositions are A333223.
%Y A335279 Cf. A000120, A003022, A029931, A066099, A070939, A124767, A124770, A325770, A334299, A334968.
%K A335279 nonn
%O A335279 1,3
%A A335279 _Gus Wiseman_, Jun 03 2020