A371961 -id:A371961 - cp's OEIS frontend

A371962 Inverse permutation to A371961.

0, 1, 3, 2, 6, 7, 4, 5, 14, 12, 13, 15, 8, 10, 11, 9, 28, 29, 24, 25, 26, 27, 30, 31, 16, 17, 20, 21, 22, 23, 18, 19, 60, 56, 57, 61, 48, 52, 53, 49, 50, 54, 55, 51, 62, 58, 59, 63, 32, 36, 37, 33, 44, 40, 41, 45, 46, 42, 43, 47, 34, 38, 39, 35, 120, 121, 112

Offset: 0

Rémy Sigrist, Apr 14 2024

			A371961(42) = 57, so a(57) = 42.

Rémy Sigrist, Table of n, a(n) for n = 0..8191
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A371961.

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A371944 The binary expansion of a(n) corresponds to the ordinal transform (reduced modulo 2) of the binary expansion of n.

Original entry on oeis.org

0, 1, 3, 2, 6, 6, 5, 5, 13, 12, 12, 13, 10, 11, 11, 10, 26, 26, 25, 25, 25, 25, 26, 26, 21, 21, 22, 22, 22, 22, 21, 21, 53, 52, 52, 53, 50, 51, 51, 50, 50, 51, 51, 50, 53, 52, 52, 53, 42, 43, 43, 42, 45, 44, 44, 45, 45, 44, 44, 45, 42, 43, 43, 42, 106, 106

Offset: 0

Rémy Sigrist, Apr 13 2024

Leading zeros are ignored.

All terms belong to A063037.

			For n = 43: the binary expansion of 43 is "101011", the corresponding ordinal transform is "1, 1, 2, 2, 3, 4", reducing modulo 2 yields "110010", the binary expansion of a(43), so a(43) = 50.

Rémy Sigrist, Table of n, a(n) for n = 0..8191
OEIS Wiki, Ordinal transform
Index entries for sequences related to binary expansion of n

Cf. A063037, A070939, A371961.

{0}~Join~Array[(c[0] = 1; c[1] = 1; FromDigits[Map[Mod[c[#]++, 2] &, IntegerDigits[#, 2] ], 2]) &, 120] (* Michael De Vlieger, Apr 16 2024 *)

a(n) = { my (b = binary(n), f = vector(2)); for (i = 1, #b, b[i] = f[1+b[i]]++;); fromdigits(b % 2, 2); }

A070939(a(n)) = A070939(n).

a(floor(n/2)) = floor(a(n)/2).

cp's OEIS Frontend

A371962 Inverse permutation to A371961.

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