A187126 Triangular numbers k*(k+1)/2 mod 1000, sorted and uniqued.

0, 1, 3, 5, 6, 10, 11, 15, 16, 20, 21, 25, 26, 28, 30, 31, 35, 36, 40, 41, 45, 46, 50, 51, 55, 56, 60, 61, 65, 66, 70, 71, 75, 76, 78, 80, 81, 85, 86, 90, 91, 95, 96, 100, 101, 105, 106, 110, 111, 115, 116, 120, 121, 125, 126, 128, 130, 131, 135, 136, 140

Offset: 1

Author

Shyam Sunder Gupta, Aug 30 2013

Keywords

• base
• fini
• full
• nonn

Comments

Possible last three digits of triangular numbers k*(k+1)/2 (leading zeros omitted).

All triangular numbers less than 1000 belong to this sequence. The sequence is finite with 424 terms: a(424)=996 is the last term.

Examples

			The last three digits of k*(k+1)/2 can be 000, 001, 003, 021, 140, etc., but not 002, 004, 012, 139 etc.
		

Links

• Shyam Sunder Gupta, Table of n, a(n) for n = 1..424

Crossrefs

Cf. A000217, A122986.

Programs

Mathematica

Union[Table[Mod[n*(n + 1)/2, 1000], {n, 1, 1000}]]