A352783 Inverse permutation to A352782.

0, 1, 2, 5, 3, 9, 10, 21, 4, 13, 18, 37, 11, 41, 42, 85, 6, 17, 26, 53, 19, 73, 74, 149, 20, 45, 82, 165, 43, 169, 170, 341, 7, 25, 34, 69, 27, 105, 106, 213, 36, 77, 146, 293, 75, 297, 298, 597, 22, 81, 90, 181, 83, 329, 330, 661, 84, 173, 338, 677, 171, 681

Offset: 0

Author

Rémy Sigrist, Apr 02 2022

Keywords

• nonn
• base

Examples

			A352782(42) = 14, so a(14) = 42.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000120, A069010, A352782.

Programs

PARI

a(n) = { my (v=0, s=1, e, oz, o); while (n, n\=2^e=1+valuation(n, 2); oz = (sqrtint(e*8)+1)\2; o = e-binomial((sqrtint(8*e)+1)\2, 2); v += s * (2^o-1) * 2^(oz-o); s *= 2^(1+oz)); v }

Formula

A069010(a(n)) = A000120(n).

a(2^k) = A023758(k+1) for any k >= 0.