A376733 a(1) = 0; for any any n > 1, if A376637(n) starts with a digit 1 then a(n) = 2*a(A376676(n)) otherwise a(n) = 2*a(A376676(n)) + 1.

0, 1, 2, 4, 5, 3, 10, 8, 9, 11, 18, 6, 20, 21, 7, 19, 22, 36, 16, 40, 41, 17, 37, 23, 14, 12, 13, 15, 42, 82, 38, 44, 32, 72, 73, 33, 45, 39, 83, 43, 74, 34, 46, 80, 81, 47, 35, 75, 26, 30, 28, 24, 25, 29, 31, 27, 78, 164, 84, 144, 64, 88, 89, 65, 145, 85, 165

Offset: 1

Author

Rémy Sigrist, Oct 03 2024

Keywords

• nonn
• base

Comments

The binary expansion of a(n) encodes the position of A376637(n) within the binary tree underlying A376676 (see illustration in Links section).

This sequence is a bijection from the positive integers to the nonnegative integers.

Examples

			See illustration in Links section.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10048
• Rémy Sigrist, Illustration of terms < 32 (where b = A376637)
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A070939, A376637, A376676, A376698.

Programs

PARI

\\ See Links section.

Formula

A070939(a(n)) = A376698(n) for any n > 0.