A068127 Triangular numbers with sum of digits = 3.

3, 21, 120, 210, 300, 10011, 20100, 2001000, 200010000, 20000100000, 2000001000000, 200000010000000, 20000000100000000, 2000000001000000000, 200000000010000000000, 20000000000100000000000, 2000000000001000000000000, 200000000000010000000000000, 20000000000000100000000000000

Offset

1,1

Comments

The sequence is unbounded, as the (2*10^k)-th triangular number is a term.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..504

Mathematica

t = {}; Do[tri = n*(n+1)/2; If[Total[IntegerDigits[tri, 10]] == 3, AppendTo[t, tri]], {n, 1000000}]; t (* T. D. Noe, Jun 05 2012 *)
Select[Accumulate[Range[2*10^6]], Total[IntegerDigits[#]]==3&] (* Harvey P. Dale, Jun 22 2021 *)
Sort @ Select[Plus @@@ (10^Select[Tuples[Range[0, 29], 3], Min[Differences[#]] >= 0 &]), IntegerQ[Sqrt[8*# + 1]] &] (* Amiram Eldar, May 19 2022 *)

Prog

(Python)
from math import isqrt
from itertools import count, islice
def istri(n): return (lambda x: x == isqrt(x)**2)(8*n+1)
def agen(): yield from filter(istri, (10**i + 10**j + 10**k for i in count(0) for j in range(i+1) for k in range(j+1)))
print(list(islice(agen(), 20))) # Michael S. Branicky, May 14 2022

Crossrefs

Cf. A000217, A004157, A052217.

Sequence in context: A084159 A283421 A117512 * A247247 A322185 A171137

Adjacent sequences: A068124 A068125 A068126 * A068128 A068129 A068130

Keyword

base,easy,nonn

Author

Amarnath Murthy, Feb 21 2002

Extensions

More terms from Sascha Kurz, Mar 06 2002

One additional term (a(12)) from Harvey P. Dale, May 14 2022

More terms and offset changed to 1 from Michael S. Branicky, May 14 2022

Status

approved