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

Author

Rémy Sigrist, Feb 06 2023

Keywords

• nonn
• base
• tabf

Comments

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

Examples

			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
		

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

Crossrefs

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

Programs

PARI

See Links section.

Formula

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

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

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