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

Author

Amarnath Murthy, Feb 21 2002

Keywords

• base
• easy
• nonn

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

Crossrefs

Cf. A000217, A004157, A052217.

Programs

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 *)

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

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