A068129 Triangular numbers with sum of digits = 10.

28, 55, 91, 136, 190, 253, 325, 406, 703, 820, 1081, 1225, 1540, 1711, 2080, 2701, 3160, 3403, 5050, 7021, 10153, 11026, 12403, 15400, 17020, 20503, 21115, 23005, 24310, 32131, 41041, 51040, 52003, 60031, 72010, 80200, 90100, 106030, 110215

Offset: 1

Author

Amarnath Murthy, Feb 21 2002

Keywords

• base
• easy
• nonn

Comments

1. The sequence is unbounded, as the (2*10^k +2)-th triangular number is a term. 2. The sum of the digits of triangular numbers in most cases is a triangular number. 3. Conjecture: For every triangular number T there exist infinitely many triangular numbers with sum of digits = T.

The second assertion above is wrong. Out of the first 100,000 triangular numbers, only 26,046 have a sum of their digits equal to a triangular number. - Harvey P. Dale, Jun 07 2017

Links

• Robert Israel, Table of n, a(n) for n = 1..164

Crossrefs

Intersection of A000217 and A052224.

Cf. A062688, A068127, A068128.

Programs

Maple

for i from 1 to 9 do S[1,i]:= [i] od: S[1,10]:= []:
R:= NULL: count:= 0:
for d from 2 while count < 100 do
  for i from 1 to 10 do
    S[d,i]:= [seq(op(map(t -> 10*t + j, S[d-1,i-j])),j=0..i-1)];
  od:
  V:= select(t -> issqr(8*t+1), S[d,10]);
  if nops(V) > 0 then
    V:= sort(V);
    R:= R,op(V); count:= count+nops(V);
  fi
od:
R; # Robert Israel, May 15 2025

Mathematica

Select[Accumulate[Range[1000]],Total[IntegerDigits[#]]==10&] (* Harvey P. Dale, Jun 07 2017 *)

Extensions

More terms from Sascha Kurz, Mar 06 2002

Offset changed by Andrew Howroyd, Sep 17 2024