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

Author

Rémy Sigrist, Jul 04 2018

Keywords

• nonn
• base

Examples

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

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8191
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

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

Programs

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]

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]