A380122 a(n) is the number of integers m (possibly negative) such that the nonzero digits in the nonadjacent form for m appear in the nonadjacent form for n.

1, 2, 2, 4, 2, 4, 4, 4, 2, 4, 4, 8, 4, 8, 4, 4, 2, 4, 4, 8, 4, 8, 8, 8, 4, 8, 8, 8, 4, 8, 4, 4, 2, 4, 4, 8, 4, 8, 8, 8, 4, 8, 8, 16, 8, 16, 8, 8, 4, 8, 8, 16, 8, 16, 8, 8, 4, 8, 8, 8, 4, 8, 4, 4, 2, 4, 4, 8, 4, 8, 8, 8, 4, 8, 8, 16, 8, 16, 8, 8, 4, 8, 8, 16, 8

Offset

0,2

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Joerg Arndt, Matters Computational (The Fxtbook), pages 61-62.

Wikipedia, Non-adjacent form

Formula

a(n) = 2^A000120(A184617(n)) = A001316(A184617(n)).

Example

The nonadjacent form for 25 is "10T001" and has 3 nonzero digits, so a(25) = 2^3 = 8.

Prog

(PARI) a(n) = { my (v = 1); while (n, if (n%2, n -= 2 - (n%4); v *= 2; ); n \= 2; ); return (v); }

Crossrefs

Cf. A000120, A001316, A184617, A380123 (corresponding m's).

Sequence in context: A082991 A214212 A100008 * A102763 A054844 A057936

Adjacent sequences: A380119 A380120 A380121 * A380123 A380124 A380125

Keyword

nonn,base

Author

Rémy Sigrist, Jan 12 2025

Status

approved