A335279 - OEIS

A335279

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

%I #7 Jun 04 2020 06:40:04

%S 0,1,3,5,11,15,23,27,37,47,55,107,111,119,155,215,223,239,411,431,471,

%T 479,495,549,631,943,951,959,991,1647,1887,1967,1983,2015,2543,2935,

%U 3703,3807,3935,3967,4031,6639,6895,7407,7871,7903,8063,8127,10207,13279

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

%e The sequence together with the corresponding compositions begins:

%e 0: () 215: (1,2,2,1,1,1)

%e 1: (1) 223: (1,2,1,1,1,1,1)

%e 3: (1,1) 239: (1,1,2,1,1,1,1)

%e 5: (2,1) 411: (1,3,1,2,1,1)

%e 11: (2,1,1) 431: (1,2,2,1,1,1,1)

%e 15: (1,1,1,1) 471: (1,1,2,2,1,1,1)

%e 23: (2,1,1,1) 479: (1,1,2,1,1,1,1,1)

%e 27: (1,2,1,1) 495: (1,1,1,2,1,1,1,1)

%e 37: (3,2,1) 549: (4,3,2,1)

%e 47: (2,1,1,1,1) 631: (3,1,1,2,1,1,1)

%e 55: (1,2,1,1,1) 943: (1,1,2,2,1,1,1,1)

%e 107: (1,2,2,1,1) 951: (1,1,2,1,2,1,1,1)

%e 111: (1,2,1,1,1,1) 959: (1,1,2,1,1,1,1,1,1)

%e 119: (1,1,2,1,1,1) 991: (1,1,1,2,1,1,1,1,1)

%e 155: (3,1,2,1,1) 1647: (1,3,1,2,1,1,1,1)

%e The subsequences for n = 0, 1, 3, 5, 11, 15, 23, 27 are the following (0 = empty partition):

%e 0 0 0 0 0 0 0 0 0 0

%e 1 1 1 1 1 1 1 1 1

%e 11 2 2 11 2 2 2 2

%e 21 11 111 11 11 3 11

%e 21 1111 21 12 21 21

%e 211 111 21 32 111

%e 211 121 321 211

%e 2111 211 1111

%e 1211 2111

%e 21111

%t stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;

%t seq=Table[Length[Union[ReplaceList[stc[n],{___,s___,___}:>{s}]]],{n,0,1000}];

%t Table[Position[seq,i][[1,1]]-1,{i,First/@Gather[seq]}]

%Y Positions of first appearances in A124771.

%Y Compositions where every subinterval has a different sum are A333222.

%Y Knapsack compositions are A333223.

%Y Cf. A000120, A003022, A029931, A066099, A070939, A124767, A124770, A325770, A334299, A334968.

%K nonn

%O 1,3

%A _Gus Wiseman_, Jun 03 2020