A062099 Triangular numbers whose sum of digits is a triangular number.

0, 1, 3, 6, 10, 15, 21, 28, 55, 78, 91, 105, 120, 136, 190, 210, 231, 253, 276, 300, 325, 406, 465, 528, 703, 780, 820, 861, 1081, 1176, 1225, 1275, 1540, 1596, 1653, 1711, 1770, 2080, 2211, 2346, 2701, 2775, 2850, 3003, 3160, 3403, 3486, 3570, 3741, 3828

Offset: 1

Author

Amarnath Murthy, Jun 16 2001

Keywords

• nonn
• base
• easy

Examples

			a(8) = 28 is a triangular number and the sum of digits 10 is also a triangular number.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A187744 and A000217.

Programs

Magma

[ t: n in [0..90] | IsSquare(8*s+1) where s is &+Intseq(t) where t is n*(n+1) div 2 ];  // Bruno Berselli, May 27 2011

Mathematica

With[{trnos=Accumulate[Range[0,200]]},Select[trnos,MemberQ[trnos, Total[ IntegerDigits[ #]]]&]] (* Harvey P. Dale, Feb 26 2013 *)

PARI

{ for(m=0, 100, my(k=binomial(m+1,2)); if(ispolygonal(sumdigits(k),3), print1(k, ", "))) } \\ Harry J. Smith, Aug 01 2009

Extensions

More terms from Erich Friedman, Jun 20 2001