A382245 Lexicographically earliest sequence of distinct nonnegative integers such that the product of two consecutive terms is always a triangular number (A000217).

0, 1, 3, 2, 5, 9, 4, 7, 13, 6, 11, 21, 10, 12, 23, 45, 14, 15, 8, 17, 33, 16, 31, 61, 30, 26, 51, 25, 49, 24, 22, 43, 85, 42, 28, 55, 18, 35, 44, 87, 19, 37, 73, 36, 56, 111, 98, 195, 62, 69, 34, 39, 20, 41, 81, 40, 52, 103, 205, 66, 58, 115, 57, 29, 59, 117

Offset: 0

Author

Rémy Sigrist, Mar 19 2025

Keywords

• nonn

Comments

This sequence has similarities with A026741: in both sequences, the product of two consecutive terms is always a triangular number; here all terms are distinct, there all products of two consecutive terms are distinct.

Examples

			The initial terms are:
  n   a(n)  a(n)*a(n+1)
  --  ----  ------------------
   0     0     0 = A000217(0)
   1     1     3 = A000217(2)
   2     3     6 = A000217(3)
   3     2    10 = A000217(4)
   4     5    45 = A000217(9)
   5     9    36 = A000217(8)
   6     4    28 = A000217(7)
   7     7    91 = A000217(13)
   8    13    78 = A000217(12)
   9     6    66 = A000217(11)
  10    11   231 = A000217(21)
  11    21   210 = A000217(20)
  12    10   120 = A000217(15)
  13    12   276 = A000217(23)
  14    23  1035 = A000217(45)
  15    45   630 = A000217(35)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, PARI program

Crossrefs

Cf. A000217, A026741, A077220, A213005, A382244.

Programs

PARI

\\ See Links section.