A366379 -id:A366379 - cp's OEIS frontend

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

Antti Karttunen, Oct 22 2023

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

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

Cf. also A118967.

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)); };

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).

A366378 Numbers k such that A057889(k) == k (mod 3), where A057889 is the bijective bit-reverse.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 36, 38, 39, 40, 42, 45, 46, 48, 50, 51, 54, 56, 57, 58, 60, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 87, 89, 90, 91, 92, 93, 95, 96, 97, 99, 100, 101, 102, 103

Offset: 1

Antti Karttunen, Oct 22 2023

nonn

Cf. A030101, A057889, A366379 (complement), A366389.

Subsequences: A000079, A008585, A057890.

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)));
isA366378(n) = !((A057889(n)-n)%3);

cp's OEIS Frontend

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

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