A331166 a(n) = min(n, A057889(n)), where A057889 is bijective base-2 reverse.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 19, 22, 27, 28, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 37, 42, 43, 44, 45, 46, 47, 48, 35, 38, 51, 44, 43, 54, 55, 56, 39, 46, 55, 60, 47, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 69, 74, 83, 84, 85, 86, 87, 88, 77, 90, 91, 92, 93, 94, 95, 96, 67, 70

Offset: 0

Author

Antti Karttunen, Jan 12 2020

Keywords

• nonn
• base

Comments

There is a large number of sequences b, related to binary expansion of n (A007088), for which it holds that b(n) = b(a(n)) for all n >= 0 (or n >= 1). For example, we have:

For all i, j:

a(i) = a(j) => A002487(i) = A002487(j),

a(i) = a(j) => A005811(i) = A005811(j),

a(i) = a(j) => A286622(i) = A286622(j) => A000120(i) = A000120(j).

For all i, j > 0:

a(i) = a(j) => A007814(i) = A007814(j),

a(i) = a(j) => A280505(i) = A280505(j),

a(i) = a(j) => A305788(i) = A305788(j) => A091222(i) = A091222(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000120, A002487, A005811, A007088, A007814, A030101, A057889, A091222, A280505, A286622, A305788.

Cf. also A330740, A331167, A331173.

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)));
A331166(n) = min(n, A057889(n));

Formula

a(n) = min(n, A057889(n)).