A374817 Irregular table T(n, k), n > 0, k = 1..A000005(n), read by rows; the n-th row lists the numbers m such that A003991(m) = n.

1, 2, 3, 4, 6, 5, 7, 10, 11, 15, 8, 9, 16, 21, 22, 28, 12, 14, 29, 36, 13, 37, 45, 17, 20, 46, 55, 56, 66, 18, 19, 23, 27, 67, 78, 79, 91, 30, 35, 92, 105, 24, 26, 106, 120, 25, 38, 44, 121, 136, 137, 153, 31, 34, 47, 54, 154, 171, 172, 190, 32, 33, 57, 65, 191, 210

Offset

1,2

Comments

A003991 corresponds to a square array, but we consider it here as a flat sequence (when its values are read according along its antidiagonals).

This sequence is a permutation of the positive integers with inverse A374818.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..7069 (rows for n = 1..1000 flattened)

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Formula

T(n, A000005(n)) = A000217(n).

Example

Table T(n, k) begins:
  n   n-th row
  --  ----------------------
   1  1
   2  2, 3
   3  4, 6
   4  5, 7, 10
   5  11, 15
   6  8, 9, 16, 21
   7  22, 28
   8  12, 14, 29, 36
   9  13, 37, 45
  10  17, 20, 46, 55
  11  56, 66
  12  18, 19, 23, 27, 67, 78
  13  79, 91
  14  30, 35, 92, 105
  15  24, 26, 106, 120

Prog

(PARI) \\ See Links section.

Crossrefs

See A374799 for a similar sequence.

Cf. A000005, A000217, A003991, A374818 (inverse).

Sequence in context: A371360 A175004 A361941 * A191734 A191443 A136175

Adjacent sequences: A374814 A374815 A374816 * A374818 A374825 A374826

Keyword

nonn,tabf

Author

Rémy Sigrist, Jul 21 2024

Status

approved