OFFSET

0,6

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 nonfixed point in a composition c is an index i such that c_i != i.

EXAMPLE

The 169th composition in standard order is (2,2,3,1), with nonfixed points {1,4}, so a(169) = 2.

MATHEMATICA

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

pnq[y_]:=Length[Select[Range[Length[y]], #!=y[[#]]&]];

Table[pnq[stc[n]], {n, 0, 100}]

CROSSREFS

A011782 counts compositions.

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 27 2022

STATUS

approved