A367307 -id:A367307 - cp's OEIS frontend

A372317 For any n > 0 with leading ternary digit h = A122586(n), reverse digits in blocks in ternary expansion of n where blocks are separated by h's; a(0) = 0.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 12, 13, 14, 11, 16, 17, 18, 21, 20, 19, 22, 23, 24, 25, 26, 27, 28, 45, 30, 31, 32, 33, 46, 51, 36, 37, 42, 39, 40, 41, 38, 43, 44, 29, 34, 47, 48, 49, 50, 35, 52, 53, 54, 63, 56, 57, 66, 65, 60, 61, 62, 55, 64, 59, 58, 67

Offset: 0

Rémy Sigrist, Apr 27 2024

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

This sequence has infinitely many fixed points (A125292, among others).

			For n = 5323: the ternary expansion of 5323 is "21022011", the corresponding leading digit is "2", we have three blocks: "10", "" and "011", their reversals are: "01", "" and "110", so the ternary expansion of a(5323) is "20122110", and a(5323) = 4845.

See A367307 and A372318 for similar sequences.

Cf. A122586, A125292.

a(n, base = 3) = { my (d = digits(n, base), i = 1); for (j = 2, #d+1, if (j==#d+1 || d[i]==d[j], my (ii = i+1, jj = j-1); while (ii < jj, [d[ii], d[jj]] = [d[jj], d[ii]]; ii++; jj--;); i = j;);); fromdigits(d, base); }

A377440 Lexicographically latest sequence of nonnegative integers such that for any n >= 0, A265263(n) = A265263(a(n)).

Original entry on oeis.org

0, 1, 3, 2, 6, 5, 4, 7, 12, 10, 9, 13, 8, 11, 15, 14, 24, 20, 18, 25, 17, 21, 27, 26, 16, 19, 23, 22, 30, 29, 28, 31, 48, 40, 36, 49, 34, 41, 51, 50, 33, 37, 43, 42, 54, 53, 52, 55, 32, 35, 39, 38, 46, 45, 44, 47, 60, 58, 57, 61, 56, 59, 63, 62, 96, 80, 72, 97

Offset: 0

Rémy Sigrist, Oct 28 2024

This sequence is a self-inverse permutation of the nonnegative integers that preserves the binary length.

			The first terms are:
  n   a(n)  A265263(n)  A265263(a(n))
  --  ----  ----------  -------------
   0     0           0              0
   1     1           1              1
   2     3           2              2
   3     2           2              2
   4     6           4              4
   5     5           4              4
   6     4           4              4
   7     7           5              5
   8    12           8              8
   9    10           8              8
  10     9           8              8
  11    13           9              9
  12     8           8              8
  13    11           9              9
  14    15          10             10
  15    14          10             10

Rémy Sigrist, Table of n, a(n) for n = 0..8191
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A265263, A367307.

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A372317 For any n > 0 with leading ternary digit h = A122586(n), reverse digits in blocks in ternary expansion of n where blocks are separated by h's; a(0) = 0.

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