A316472 Inverse permutation to A316385.

1, 3, 2, 5, 7, 6, 4, 9, 11, 13, 15, 10, 14, 12, 8, 17, 19, 21, 23, 25, 27, 29, 31, 18, 22, 26, 30, 20, 28, 24, 16, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 34, 38, 42, 46, 50, 54, 58, 62, 36, 44, 52, 60, 40, 56, 48, 32, 65, 67, 69, 71

Offset

1,2

Links

Rémy Sigrist, Table of n, a(n) for n = 1..8191

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = (2*b(n) + 1)*2^(L(n) - L(b(n)) - 1) where b(n) = A053645(A153142(n)) and where L(n) = A000523(n) for n > 0 with L(0) = -1. - Mikhail Kurkov, Sep 09 2023 [verification needed]

Example

A316385(42) = 50 hence a(50) = 42.

Prog

(PARI) b1(n) = my(b=binary(n)); fromdigits(concat(b[1], Vecrev(vector(#b-1, k, b[k+1]))), 2); \\ A059893
b2(n) = if(n < 2, n, if((n + 1) == 2^logint(n + 1, 2), (n + 1) / 2, n + 1)) \\ A153152
a(n) = my(A = 2^logint(n, 2), B = b1(b2(b1(n))) - A); (2 * B + 1) * A / 2 ^ (if(B == 0, -1, logint(B, 2)) + 1) \\ Mikhail Kurkov, Sep 09 2023 [verification needed]

Crossrefs

Cf. A000523, A053645, A059893, A153142, A316385.

Sequence in context: A222209 A118320 A108918 * A360959 A341910 A341915

Adjacent sequences: A316469 A316470 A316471 * A316473 A316474 A316475

Keyword

nonn,base

Author

Rémy Sigrist, Jul 04 2018

Status

approved