A382244 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, n*a(n) is a triangular number (A000217).

0, 1, 3, 2, 7, 9, 6, 4, 15, 5, 12, 21, 10, 25, 27, 8, 31, 33, 35, 37, 39, 11, 24, 45, 22, 13, 30, 14, 42, 57, 26, 16, 63, 17, 67, 18, 56, 19, 75, 20, 52, 81, 28, 85, 87, 23, 51, 93, 95, 97, 99, 46, 40, 105, 60, 90, 36, 29, 66, 117, 54, 121, 69, 32, 127, 84, 58

Offset: 0

Author

Rémy Sigrist, Mar 19 2025

Keywords

• nonn

Comments

A self-inverse permutation of the nonnegative integers.

Examples

			The initial terms are:
  n   a(n)  n*a(n)
  --  ----  -----------------
   0     0    0 = A000217(0)
   1     1    1 = A000217(1)
   2     3    6 = A000217(3)
   3     2    6 = A000217(3)
   4     7   28 = A000217(7)
   5     9   45 = A000217(9)
   6     6   36 = A000217(8)
   7     4   28 = A000217(7)
   8    15  120 = A000217(15)
   9     5   45 = A000217(9)
  10    12  120 = A000217(15)
  11    21  231 = A000217(21)
  12    10  120 = A000217(15)
  13    25  325 = A000217(25)
  14    27  378 = A000217(27)
  15     8  120 = A000217(15)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000217, A061782, A382244.

Programs

PARI

\\ See Links section.

Formula

a(n) >= A061782(n) for any n > 0.