A268718 -id:A268718 - cp's OEIS frontend

A105081 a(n) = 1 + A003188(n - 1), n >= 1.

1, 2, 4, 3, 7, 8, 6, 5, 13, 14, 16, 15, 11, 12, 10, 9, 25, 26, 28, 27, 31, 32, 30, 29, 21, 22, 24, 23, 19, 20, 18, 17, 49, 50, 52, 51, 55, 56, 54, 53, 61, 62, 64, 63, 59, 60, 58, 57, 41, 42, 44, 43, 47, 48, 46, 45, 37, 38, 40, 39, 35, 36, 34, 33, 97, 98, 100, 99, 103, 104, 102

Offset: 1

Philippe Deléham, Apr 28 2005

A permutation of the natural numbers.

Inverse permutation: A066194.

Cf. A000069, A003188, A065621, A268718.

Nest[Join[#,Length[#]+Reverse[#]]&,{1},7] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2012 *)

def A105081(n): return 1+(n-1^ n-1>>1) # Chai Wah Wu, Jun 29 2022

(define (A105081 n) (+ 1 (A003188 (- n 1)))) ;; Antti Karttunen, Feb 14 2016

a(1) = 1, a(2^k + j) = 2^k + a(2^k - j + 1) for 1 <= j <= 2^k.
A000069(a(n)) = A065621(n).
As a composition of related permutations:
a(n) = A268718(A003188(n)). - Antti Karttunen, Feb 14 2016

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.

Original entry on oeis.org

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

Antti Karttunen, Apr 26 2018

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

Cf. A302027 (inverse).
Cf. A057889.
Cf. also A268718, A302794.

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));

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

A302794 Permutation of nonnegative integers: a(0) = 0; for n >= 1, a(n) = 1+A193231(A193231(n)-1), where A193231(n) is blue code of n.

Original entry on oeis.org

0, 1, 4, 2, 6, 3, 5, 7, 10, 12, 14, 11, 15, 13, 16, 8, 18, 9, 17, 19, 20, 21, 24, 22, 27, 25, 28, 29, 30, 32, 23, 31, 34, 36, 60, 35, 39, 37, 40, 33, 48, 41, 44, 42, 46, 38, 45, 47, 51, 49, 52, 26, 54, 56, 50, 55, 58, 63, 57, 59, 53, 61, 64, 62, 66, 71, 65, 67, 94, 69, 72, 70, 75, 73, 76, 68, 78, 80, 74, 79, 88, 81, 84, 82, 86, 43

Offset: 0

Antti Karttunen, Apr 26 2018

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

Cf. A302793 (inverse).
Cf. A193231.
Cf. also A268718, A302028.

A193231(n) = { my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2) }; \\ From A193231
A302794(n) = if(!n,n,1+A193231(A193231(n)-1));

a(0) = 0; for n >= 1, a(n) = 1+A193231(A193231(n)-1).

cp's OEIS Frontend

A105081 a(n) = 1 + A003188(n - 1), n >= 1.

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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.

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A302794 Permutation of nonnegative integers: a(0) = 0; for n >= 1, a(n) = 1+A193231(A193231(n)-1), where A193231(n) is blue code of n.

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