A265369 Self-inverse permutation of nonnegative integers: a(n) = A057889(A263273(A057889(n))).

0, 1, 2, 3, 4, 7, 6, 5, 8, 9, 10, 11, 12, 25, 26, 21, 16, 19, 18, 17, 20, 15, 22, 59, 24, 13, 14, 27, 28, 29, 30, 41, 64, 39, 58, 53, 36, 97, 98, 33, 40, 31, 66, 121, 44, 63, 50, 61, 48, 73, 46, 105, 100, 35, 54, 65, 56, 57, 34, 23, 60, 47, 82, 45, 32, 55, 42, 137, 68, 69, 142, 131, 72, 49, 74, 219, 76, 155, 234, 79, 80, 81, 62, 173

Offset: 0

Author

Antti Karttunen, Jan 02 2016

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..19684
• 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. also A265329, A265904, A266190, A266401, A266403, A266407, A266408.

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[g@ f@ g@ n, {n, 83}] (* Michael De Vlieger, Jan 04 2016, after Jean-François Alcover at A263273 and Ivan Neretin at A057889 *)

Scheme

(define (A265369 n) (A057889 (A263273 (A057889 n))))

Formula

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

As a composition of related permutations:

a(n) = A264966(A057889(n)).

a(n) = A057889(A264965(n)).

Other identities. For all n >= 0:

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