A302028 Permutation of nonnegative integers: a(0) = 0; for n >= 1, a(n) = 1+A057889(A057889(n)-1), where A057889 is a bijective bit-reverse.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 11, 12, 15, 16, 17, 18, 25, 26, 21, 20, 29, 30, 19, 22, 23, 28, 27, 24, 31, 32, 33, 34, 49, 50, 41, 36, 57, 58, 37, 38, 45, 52, 53, 40, 61, 62, 35, 42, 39, 54, 43, 44, 47, 60, 51, 46, 55, 56, 59, 48, 63, 64, 65, 66, 97, 98, 81, 68, 113, 114, 73, 70, 89, 100, 105, 72, 121, 122, 69, 74, 77, 102, 85, 76

Offset: 0

Author

Antti Karttunen, Apr 26 2018

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• David Newman, et al., New sequences from old, Discussion on SeqFan-mailing list, January 2018.
• Index entries for sequences related to binary expansion of n
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A302027 (inverse).

Cf. A057889.

Cf. also A268718, A302794.

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)));
A302028(n) = if(!n,n,1+A057889(A057889(n)-1));

Formula

a(0) = 0; for n >= 1, a(n) = 1+A057889(A057889(n)-1).