OFFSET
0,7
COMMENTS
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. See also A000120, A059893, A070939, A114994, A225620.
A fixed point of composition c is an index i such that c_i = i.
EXAMPLE
The 169th composition in standard order is (2,2,3,1), with fixed points {2,3}, so a(169) = 2.
MATHEMATICA
stc[n_]:=Differences[Prepend[Join@@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
pq[y_]:=Length[Select[Range[Length[y]], #==y[[#]]&]];
Table[pq[stc[n]], {n, 0, 100}]
CROSSREFS
A011782 counts compositions.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 26 2022
STATUS
approved