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

0,3

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6765

Index entries for sequences that are permutations of the natural numbers

Formula

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

Example

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

Prog

(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)))

Crossrefs

See A345201 for a similar sequence.

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

Sequence in context: A270426 A270425 A332212 * A085161 A085162 A182178

Adjacent sequences: A381615 A381616 A381617 * A381619 A381620 A381621

Keyword

nonn,base

Author

Rémy Sigrist, Mar 02 2025

Status

approved