A068128 Triangular numbers with sum of digits = 6.

6, 15, 105, 231, 2211, 3003, 20301, 112101, 2003001, 122000010, 200030001, 20000300001, 2000003000001, 200000030000001, 20000000300000001, 2000000003000000001, 200000000030000000001, 20000000000300000000001, 2000000000003000000000001

Offset: 1

Author

Amarnath Murthy, Feb 21 2002

Keywords

• base
• easy
• nonn

Comments

1. The sequence is unbounded, as the (2*10^k +1)-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.

Crossrefs

Intersection of A000217 and A052220.

Cf. A068127.

Programs

Mathematica

Select[Accumulate[Range[20000002]],Total[IntegerDigits[#]]==6&] (* Harvey P. Dale, Jun 05 2012 *)

Extensions

More terms from Sascha Kurz, Mar 06 2002

More terms from Sean A. Irvine, Mar 17 2023

Offset changed by Andrew Howroyd, Sep 17 2024