A381618 Reverse the Chung-Graham representation of n while preserving its trailing zeros: a(n) = A381607(A263273(A381608(n))).

0, 1, 2, 3, 4, 7, 6, 5, 8, 9, 17, 11, 12, 20, 19, 15, 16, 10, 18, 14, 13, 21, 22, 43, 24, 30, 51, 45, 38, 29, 25, 46, 32, 33, 54, 53, 41, 50, 28, 49, 40, 36, 42, 23, 44, 27, 31, 52, 48, 39, 37, 26, 47, 35, 34, 55, 56, 111, 58, 77, 132, 113, 98, 63, 64, 119, 79

Offset: 0

Author

Rémy Sigrist, Mar 02 2025

Keywords

• nonn
• base

Comments

This sequence is a self-inverse permutation of the nonnegative integers.

Examples

			The first terms, alongside their Chung-Graham representation, are:
  n   a(n)  A381579(n)  A381579(a(n))
  --  ----  ----------  -------------
   0     0           0              0
   1     1           1              1
   2     2           2              2
   3     3          10             10
   4     4          11             11
   5     7          12             21
   6     6          20             20
   7     5          21             12
   8     8         100            100
   9     9         101            101
  10    17         102            201
  11    11         110            110
  12    12         111            111
  13    20         112            211
  14    19         120            210
  15    15         121            121
  16    16         200            200
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6765
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A345201 for a similar sequence.

Cf. A000045, A263273, A381579, A381607, A381608.

Programs

PARI

A381607(n) = { my (t = Vecrev(digits(n, 3))); sum(k = 1, #t, t[k] * fibonacci(2*k)); }
A263273(n) = { my (t = 3^if (n, valuation(n, 3), 0)); t * fromdigits(Vecrev(digits(n / t, 3)), 3) }
A381608(n) = { for (k = 1, oo, my (f = fibonacci(2*k)); if (f >= n, my (v = 0); while (n, while (n >= f, n -= f; v += 3^(k-1);); f = fibonacci(2*k--);); return (v););); }
a(n) = A381607(A263273(A381608(n)))

Formula

a(n) <= A000045(2*k) iff n <= A000045(2*k).