A371257 Irregular triangle T(n, k), n >= 0, k = 1..2^A005811(n), read by rows; the n-th row lists the numbers m such that A371256(m) = n.

0, 1, 2, 3, 5, 6, 7, 4, 8, 9, 17, 18, 22, 10, 11, 15, 16, 19, 20, 21, 23, 12, 14, 24, 25, 13, 26, 27, 53, 54, 67, 28, 29, 51, 52, 55, 56, 66, 68, 30, 32, 33, 34, 46, 47, 48, 50, 57, 59, 60, 61, 64, 65, 69, 70, 31, 35, 45, 49, 58, 62, 63, 71, 36, 44, 72, 76

Offset: 0

Author

Rémy Sigrist, Mar 16 2024

Keywords

• nonn
• base
• tabf

Comments

The n-th row has 2^A005811(n) terms.

As a flat sequence, this is a permutation of the nonnegative integers, with inverse A371258.

Examples

			Triangle T(n, k) begins:
  n   n-th row
  --  --------------------------------------------------------------
   0  0
   1  1, 2
   2  3, 5, 6, 7
   3  4, 8
   4  9, 17, 18, 22
   5  10, 11, 15, 16, 19, 20, 21, 23
   6  12, 14, 24, 25
   7  13, 26
   8  27, 53, 54, 67
   9  28, 29, 51, 52, 55, 56, 66, 68
  10  30, 32, 33, 34, 46, 47, 48, 50, 57, 59, 60, 61, 64, 65, 69, 70
  11  31, 35, 45, 49, 58, 62, 63, 71
  12  36, 44, 72, 76
  13  37, 38, 42, 43, 73, 74, 75, 77
  14  39, 41, 78, 79
  15  40, 80
.
Triangle T(n, k) begins, in ternary, with row indexes in binary:
  bin(n)  n-th row in ternary
  ------  ----------------------------------------------
       0  0
       1  1, 2
      10  10, 12, 20, 21
      11  11, 22
     100  100, 122, 200, 211
     101  101, 102, 120, 121, 201, 202, 210, 212
     110  110, 112, 220, 221
     111  111, 222
    1000  1000, 1222, 2000, 2111
    1001  1001, 1002, 1220, 1221, 2001, 2002, 2110, 2112
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6560
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A371265 for a similar sequence.

Cf. A005811, A166242, A368229, A371256.

Programs

PARI

\\ See Links section.