A306993 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, n * a(n) is digitally balanced.

2, 1, 3, 11, 7, 25, 5, 23, 15, 17, 4, 13, 12, 43, 9, 47, 10, 31, 29, 37, 34, 26, 8, 39, 6, 22, 30, 81, 19, 27, 18, 95, 63, 21, 61, 67, 20, 57, 24, 70, 56, 51, 14, 55, 49, 54, 16, 53, 45, 58, 42, 65, 48, 46, 44, 41, 38, 50, 62, 149, 35, 59, 33, 191, 52, 127, 36

Offset: 1

Author

Rémy Sigrist, Mar 18 2019

Keywords

• nonn
• look
• base

Comments

Digitally balanced numbers correspond to A031443.

This sequence has similarities with A300868.

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

Examples

			The first terms, alongside the binary representation of n * a(n), are:
  n   a(n)  bin(n * a(n))
  --  ----  --------------
   1     2              10
   2     1              10
   3     3            1001
   4    11          101100
   5     7          100011
   6    25        10010110
   7     5          100011
   8    23        10111000
   9    15        10000111
  10    17        10101010
  11     4          101100
  12    13        10011100
  13    12        10011100
  14    43      1001011010
  15     9        10000111
  16    47      1011110000
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A306993
• Rémy Sigrist, Colored scatterplot of the first 10000 terms (where the color is function of A000120(n*a(n)))
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000120, A031443, A300868.

Programs

PARI

See Links section.