A316385 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, a(n) AND a(2*n) = a(n) (where AND denotes the binary AND operator).

1, 3, 2, 7, 4, 6, 5, 15, 8, 12, 9, 14, 10, 13, 11, 31, 16, 24, 17, 28, 18, 25, 19, 30, 20, 26, 21, 29, 22, 27, 23, 63, 32, 48, 33, 56, 34, 49, 35, 60, 36, 50, 37, 57, 38, 51, 39, 62, 40, 52, 41, 58, 42, 53, 43, 61, 44, 54, 45, 59, 46, 55, 47, 127, 64, 96, 65

Offset

1,2

Comments

This sequence is a permutation of the natural numbers (as odd-indexed terms are not constrained); see A316472 for the inverse sequence.

In the binary plot of the sequence, if the pixel (x, y) is on, then the pixel (2*x, y) is on.

Links

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

Rémy Sigrist, Colored scatterplot of the first 2^14-1 terms (where the color is function of the 2-adic valuation of n)

Rémy Sigrist, PARI program for A316385

Index entries for sequences that are permutations of the natural numbers

Formula

Empirically:

- a(2*k) = A004755(a(k)) for any k > 0,

- a(2*k - 1) = A004761(k + 1) for any k > 0,

- a(n) = n iff n belongs to A020989.

Example

The first terms, alongside the binary representations of a(n) and of a(2*n), are:
  n  a(n) bin(a(n)) bin(a(2n))
  -- ---- --------- ----------
   1    1         1         11
   2    3        11        111
   3    2        10        110
   4    7       111       1111
   5    4       100       1100
   6    6       110       1110
   7    5       101       1101
   8   15      1111      11111
   9    8      1000      11000
  10   12      1100      11100

Prog

(PARI) See Links section.

Crossrefs

Cf. A004755, A004761, A020989, A316472 (inverse).

Sequence in context: A255555 A191664 A118319 * A341911 A341916 A360960

Adjacent sequences: A316382 A316383 A316384 * A316386 A316387 A316388

Keyword

nonn,base

Author

Rémy Sigrist, Jul 01 2018

Status

approved