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%I #16 Sep 08 2022 08:45:03
%S 0,1,3,6,10,15,21,28,55,78,91,105,120,136,190,210,231,253,276,300,325,
%T 406,465,528,703,780,820,861,1081,1176,1225,1275,1540,1596,1653,1711,
%U 1770,2080,2211,2346,2701,2775,2850,3003,3160,3403,3486,3570,3741,3828
%N Triangular numbers whose sum of digits is a triangular number.
%H Harry J. Smith, <a href="/A062099/b062099.txt">Table of n, a(n) for n = 1..1000</a>
%e a(8) = 28 is a triangular number and the sum of digits 10 is also a triangular number.
%t With[{trnos=Accumulate[Range[0,200]]},Select[trnos,MemberQ[trnos, Total[ IntegerDigits[ #]]]&]] (* _Harvey P. Dale_, Feb 26 2013 *)
%o (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
%o (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
%Y Cf. A000217.
%K nonn,base,easy
%O 1,3
%A _Amarnath Murthy_, Jun 16 2001
%E More terms from _Erich Friedman_, Jun 20 2001
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