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

Author

Rémy Sigrist, Jan 12 2025

Keywords

• nonn
• base

Examples

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

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

Crossrefs

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

Programs

PARI

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

Formula

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