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

1,3

Links

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

Example

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

Mathematica

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

Prog

(PARI) SumD(x)= { s=0; while (x>9, s+=x-10*(x\10); x\=10); return(s + x) } { default(realprecision, 100); n=t=0; for (m=0, 10^4, s=SumD(t+=m); if (((sqrt(8*s + 1) - 1)/2)%1 == 0, write("b062099.txt", n++, " ", t); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 01 2009
(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

Crossrefs

Cf. A000217.

Sequence in context: A179653 A117520 A147846 * A115650 A025745 A175724

Adjacent sequences: A062096 A062097 A062098 * A062100 A062101 A062102

Keyword

nonn,base,easy

Author

Amarnath Murthy, Jun 16 2001

Extensions

More terms from Erich Friedman, Jun 20 2001

Status

approved