A360413 Irregular table T(n, k), n >= 0, k = 1..A002487(n+1), read by rows; the n-th row lists the numbers k such that A065361(k) = n.

0, 1, 2, 3, 4, 5, 6, 9, 7, 10, 8, 11, 12, 13, 14, 15, 18, 27, 16, 19, 28, 17, 20, 21, 29, 30, 22, 31, 23, 24, 32, 33, 36, 25, 34, 37, 26, 35, 38, 39, 40, 41, 42, 45, 54, 81, 43, 46, 55, 82, 44, 47, 48, 56, 57, 83, 84, 49, 58, 85, 50, 51, 59, 60, 63, 86, 87, 90

Offset

0,3

Comments

As a flat sequence, this is a permutation of the nonnegative integers with inverse A360414.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..9841

Rémy Sigrist, PARI program

Index entries for sequences related to Stern's sequences

Index entries for sequences that are permutations of the natural numbers

Formula

T(n, 1) = A032924(n) for any n > 0.

T(n, A002487(n+1)) = A005836(n+1).

A065361(T(n, k)) = n.

Example

Table T(n, k) begins:
  n   n-th row
  --  ------------------
   0  0
   1  1
   2  2, 3
   3  4
   4  5, 6, 9
   5  7, 10
   6  8, 11, 12
   7  13
   8  14, 15, 18, 27
   9  16, 19, 28
  10  17, 20, 21, 29, 30
  11  22, 31
  12  23, 24, 32, 33, 36
.
Table T(n, k) begins (with terms given in base 3):
  n   n-th row in base 3
  --  -------------------------
   0  0
   1  1
   2  2, 10
   3  11
   4  12, 20, 100
   5  21, 101
   6  22, 102, 110
   7  111
   8  112, 120, 200, 1000
   9  121, 201, 1001
  10  122, 202, 210, 1002, 1010
  11  211, 1011
  12  212, 220, 1012, 1020, 1100

Prog

(PARI) See Links section.

Crossrefs

Cf. A002487, A005836, A032924, A065361, A360414 (inverse).

Sequence in context: A174349 A099004 A308007 * A270194 A055170 A068384

Adjacent sequences: A360410 A360411 A360412 * A360414 A360415 A360416

Keyword

nonn,base,tabf

Author

Rémy Sigrist, Feb 06 2023

Status

approved