A265329 Self-inverse permutation of nonnegative integers: a(n) = A263273(A057889(A263273(n))).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 17, 12, 19, 26, 15, 16, 11, 18, 13, 20, 21, 22, 55, 24, 25, 14, 27, 28, 65, 30, 67, 32, 39, 38, 35, 36, 37, 34, 33, 40, 145, 42, 73, 100, 45, 46, 61, 48, 79, 226, 219, 76, 121, 54, 23, 56, 57, 70, 59, 60, 47, 82, 63, 64, 29, 66, 31, 68, 81, 58, 217, 72, 43, 74, 75, 52, 193, 174, 49, 80, 69, 62, 221

Offset: 0

Author

Antti Karttunen, Jan 02 2016

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384
• Indranil Ghosh, Python program to generate the sequence
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000035, A057889, A263273, A264965, A264966.

Cf. A266402, A266404.

Cf. also A265369.

Programs

Mathematica

f[n_] := Block[{g, h}, g[x_] := x/3^IntegerExponent[x, 3]; h[x_] := x/g@ x; If[n == 0, 0, FromDigits[Reverse@ IntegerDigits[#, 3], 3] &@ g[n] h[n]]]; g[n_] := FromDigits[Reverse@ IntegerDigits[n, 2], 2] 2^IntegerExponent[n, 2]; Prepend[#, 0] &@ Table[f@ g@ f@ n, {n, 83}] (* Michael De Vlieger, Jan 04 2016, after Jean-François Alcover at A263273 and Ivan Neretin at A057889 *)

Scheme

(define (A265329 n) (A263273 (A057889 (A263273 n))))

Formula

a(n) = A263273(A057889(A263273(n))).

As a composition of related permutations:

a(n) = A264965(A263273(n)).

a(n) = A263273(A264966(n)).

Other identities. For all n >= 0:

A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]