A366389 Variant of bijective bit-reverse of n (A057889) for which it holds that a(n) == n (mod 3).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 26, 12, 22, 14, 15, 16, 17, 18, 25, 20, 21, 13, 29, 24, 19, 11, 27, 28, 23, 30, 31, 32, 33, 34, 98, 36, 82, 50, 57, 40, 74, 42, 106, 104, 45, 58, 122, 48, 70, 38, 51, 88, 86, 54, 118, 56, 39, 46, 110, 60, 94, 62, 63, 64, 65, 66, 97, 68, 81, 49, 113, 72, 73, 41, 105, 100, 89, 114, 121

Offset: 0

Author

Antti Karttunen, Oct 22 2023

Keywords

• nonn
• look

Comments

Like A057889, also this is a self-inverse permutation of nonnegative integers.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• Index entries for sequences related to binary expansion of n
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A010872, A030101, A057889, A073675, A366378, A366379, A366390 (Dirichlet inverse), A366392.

Cf. also A118967.

Programs

PARI

A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
A073675(n) = if(valuation(n,2)%2,n/2,2*n);
A366389(n) = { my(u=A057889(n)); if(!((u-n)%3),u,A073675(u)); };

Formula

If A057889(n) == n mod 3, then a(n) = A057889(n), otherwise a(n) = A073675(A057889(n)) = A057889(A073675(n)).

For all n >= 0, A010872(a(n)) = A010872(n).