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%I #10 Sep 16 2015 00:30:52
%S 0,1,3,6,10,28,45,55,78,105,120,190,210,231,253,276,300,325,378,406,
%T 435,465,528,561,595,630,703,741,780,820,861,903,990,1035,1081,1128,
%U 1225,1275,1378,1485,1540,1596,1653,1770,1830,2016,2080,2145,2278,2346,2415
%N Triangular numbers for which the multiplicative digital root is also a triangular number.
%H Harvey P. Dale, <a href="/A116544/b116544.txt">Table of n, a(n) for n = 1..1000</a>
%t a = {}; For[n = 0, n < 100, n++, b = n*(n + 1)/2; While[b > 9, b = Times @@ IntegerDigits[b]]; If[Length[Intersection[{b}, {0, 1, 3, 6}]] == 1, AppendTo[a, n*(n + 1)/2]]]; a (* _Stefan Steinerberger_, Jan 02 2008 *)
%t dr[n_]:=NestWhile[Times@@IntegerDigits[#]&,n,#>9&]; With[{trnos= Accumulate[Range[0,80]]},Select[trnos,MemberQ[trnos,dr[#]]&]] (* _Harvey P. Dale_, Nov 02 2011 *)
%K nonn,base
%O 1,3
%A Luc Stevens (lms022(AT)yahoo.com), Apr 03 2006
%E More terms from _Stefan Steinerberger_, Jan 02 2008
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