A341335 -id:A341335 - cp's OEIS frontend

A341336 Inverse permutation to A341335.

0, 1, 3, 2, 7, 6, 5, 4, 14, 15, 12, 13, 11, 10, 9, 8, 29, 28, 31, 30, 25, 24, 27, 26, 23, 22, 21, 20, 19, 18, 17, 16, 59, 58, 57, 56, 63, 62, 61, 60, 50, 51, 48, 49, 54, 55, 52, 53, 46, 47, 44, 45, 42, 43, 40, 41, 39, 38, 37, 36, 35, 34, 33, 32, 119, 118, 117

Offset: 0

Rémy Sigrist, Apr 25 2021

			A341335(42) = 52, so a(52) = 42.

Cf. A341335.

a(n) = { my (c=binary(n), b=c); for (m=1, #b, fordiv (m, d, if (d

A371974 For any positive integer n with binary expansion (b_1, ..., b_w) (where b_1 = 1), the binary expansion of a(n) is (c_1, ..., c_w) with c_k = (Sum_{i = 1 mod (w+1-k)} b_i) mod 2 for k = 1..w; a(0) = 0.

Original entry on oeis.org

0, 1, 3, 2, 7, 4, 6, 5, 15, 10, 12, 9, 14, 11, 13, 8, 31, 20, 26, 17, 28, 23, 25, 18, 30, 21, 27, 16, 29, 22, 24, 19, 63, 46, 52, 37, 58, 43, 49, 32, 60, 45, 55, 38, 57, 40, 50, 35, 62, 47, 53, 36, 59, 42, 48, 33, 61, 44, 54, 39, 56, 41, 51, 34, 127, 88, 110

Offset: 0

Rémy Sigrist, Apr 14 2024

This sequence is a permutation of the nonnegative integers with inverse A371975.

			For n = 42: the binary expansion of 42 is "101010":
          b_1 b_2 b_3 b_4 b_5 b_6
           1   0   1   0   1   0
     c_1 = 1                      = 1 mod 2
     c_2 = 1                 + 0  = 1 mod 2
     c_3 = 1             + 1      = 0 mod 2
     c_4 = 1         + 0          = 1 mod 2
     c_5 = 1     + 1     + 1      = 1 mod 2
     c_6 = 1 + 0 + 1 + 0 + 1 + 0  = 1 mod 2
- so the binary expansion of a(42) is "110111", and a(42) = 55.

See A341335 and A371976 for similar sequences.

Cf. A010060, A070939, A371975 (inverse).

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

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

a(n) mod 2 = A010060(n).

cp's OEIS Frontend

A341336 Inverse permutation to A341335.

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