A331274 a(n) is the greatest binary anagram of n not yet in the sequence.

1, 2, 3, 4, 6, 5, 7, 8, 12, 10, 14, 9, 13, 11, 15, 16, 24, 20, 28, 18, 26, 25, 30, 17, 22, 21, 29, 19, 27, 23, 31, 32, 48, 40, 56, 36, 52, 50, 60, 34, 49, 44, 58, 42, 57, 54, 62, 33, 41, 38, 53, 37, 51, 46, 61, 35, 45, 43, 59, 39, 55, 47, 63, 64, 96, 80, 112

Offset

1,2

Comments

Leading zeros are ignored.

This sequence is a self-inverse permutation of the natural numbers.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..8192

Rémy Sigrist, Colored scatterplot of the first 2^13 terms (where the color is function of the Hamming weight of n)

Rémy Sigrist, PARI program for A331274

Index entries for sequences that are permutations of the natural numbers

Formula

a(A187769(n, k)) = a(A187769(n, A007318(n-1)+1-k) for any n > 0 and k = 1..A007318(n-1).

Example

The first terms, in decimal and in binary, are:
  n   a(n)  bin(n)  bin(a(n))
  --  ----  ------  ---------
   1     1       1          1
   2     2      10         10
   3     3      11         11
   4     4     100        100
   5     6     101        110
   6     5     110        101
   7     7     111        111
   8     8    1000       1000
   9    12    1001       1100
  10    10    1010       1010
  11    14    1011       1110
  12     9    1100       1001
  13    13    1101       1101
  14    11    1110       1011
  15    15    1111       1111

Prog

(PARI) See Links section.

Crossrefs

Cf. A007318, A187769, A298847, A331275 (ternary analog).

Sequence in context: A333776 A305410 A059893 * A269365 A269366 A361481

Adjacent sequences: A331271 A331272 A331273 * A331275 A331276 A331277

Keyword

nonn,look,base

Author

Rémy Sigrist, Jan 13 2020

Status

approved