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

0,3

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

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).

Prog

(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)); };

Crossrefs

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

Cf. also A118967.

Sequence in context: A106604 A095205 A344325 * A161978 A132579 A004850

Adjacent sequences: A366386 A366387 A366388 * A366390 A366391 A366392

Keyword

nonn,look

Author

Antti Karttunen, Oct 22 2023

Status

approved