

A357708


Numbers k such that the kth composition in standard order has sum equal to twice its maximum part.


1



3, 10, 11, 13, 14, 36, 37, 38, 39, 41, 44, 50, 51, 52, 57, 60, 136, 137, 138, 139, 140, 141, 142, 143, 145, 152, 162, 163, 168, 177, 184, 196, 197, 198, 199, 200, 209, 216, 226, 227, 232, 241, 248, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539
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OFFSET

1,1


COMMENTS

The kth composition in standard order (graded reverselexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.


LINKS



EXAMPLE

The terms and corresponding compositions begin:
3: (1,1)
10: (2,2)
11: (2,1,1)
13: (1,2,1)
14: (1,1,2)
36: (3,3)
37: (3,2,1)
38: (3,1,2)
39: (3,1,1,1)
41: (2,3,1)
44: (2,1,3)
50: (1,3,2)
51: (1,3,1,1)


MATHEMATICA

stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Select[Range[0, 1000], Max@@stc[#]==Total[stc[#]]/2&]


CROSSREFS

See link for sequences related to standard compositions.
A124767 counts runs in standard compositions.
A356844 ranks compositions with at least one 1.


KEYWORD

nonn


AUTHOR



STATUS

approved



