A302027 Permutation of nonnegative integers: a(0) = 0; for n >= 1, a(n) = A057889(1+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, 22, 21, 26, 27, 30, 19, 20, 29, 28, 23, 24, 31, 32, 33, 34, 49, 38, 41, 42, 51, 46, 37, 50, 53, 54, 43, 58, 55, 62, 35, 36, 57, 44, 45, 52, 59, 60, 39, 40, 61, 56, 47, 48, 63, 64, 65, 66, 97, 70, 81, 74, 99, 78, 73, 82, 101, 86, 83, 90, 103, 94, 69, 98, 105, 102, 85

Offset: 0

Author

Antti Karttunen, Apr 26 2018

Keywords

• nonn
• base
• look

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. A302028 (inverse).

Cf. A057889.

Cf. also A268717, A302793.

Programs

Mathematica

f[n_] := FromDigits[Reverse[IntegerDigits[n, 2]], 2]*2^IntegerExponent[n, 2]; Fold[Append[#1, f[1 + f[#2 - 1]]] &, {0, 1}, Range[2, 85]] (* Michael De Vlieger, Apr 27 2018, after Ivan Neretin at A057889 *)

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)));
A302027(n) = if(!n,n,A057889(1+A057889(n-1)));

Formula

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