OFFSET
0,4
COMMENTS
A composition of n is a finite sequence of positive integers summing to n. The k-th composition in standard order (graded reverse-lexicographic, 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
Composition 87 in standard order is (2,2,1,1,1), so a(87) = 2.
MATHEMATICA
stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Table[If[n==0, 0, First[Length/@Split[stc[n]]]], {n, 0, 100}]
CROSSREFS
See link for sequences related to standard compositions.
This is the first part of row n of A333769.
The last instead of first run-length is A357181.
A051903 gives maximal part in prime signature.
A061395 gives maximal prime index.
A124767 counts runs in standard compositions.
A286470 gives maximal difference of prime indices.
A353847 ranks run-sums of standard compositions.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 24 2022
STATUS
approved