%I #13 May 13 2013 01:54:08
%S 0,1,6,10,105,120,153,190,210,231,300,351,406,465,630,703,741,780,820,
%T 903,990,1035,1081,1540,1770,1830,2016,2080,2701,2850,3003,3081,3160,
%U 3240,3403,3570,4005,4095,4560,4950,5050,5460,6105,6670,6786,6903,7021,7140
%N Triangular numbers for which the product of the digits is a hexagonal number.
%C Presumably a(n) ~ 0.5 n^2 since I assume the product of the digits of almost all triangular numbers is 0. - _Charles R Greathouse IV_, Dec 20 2012
%H Charles R Greathouse IV, <a href="/A117310/b117310.txt">Table of n, a(n) for n = 0..10000</a>
%e 153 is in the sequence because (1) it is a triangular number and (2) the product of its digits 1*5*3=15 is a hexagonal number.
%t nn=200;With[{hex=Table[n(2n-1),{n,0,nn}]},Select[Accumulate[ Range[ 0,nn]], MemberQ[hex,Times@@IntegerDigits[#]]&]](* _Harvey P. Dale_, Dec 20 2012 *)
%o (PARI) is(n)=if(ispolygonal(n, 3), my(v=digits(n)); ispolygonal(prod(i=1, #v, v[i]), 6), 0) \\ _Charles R Greathouse IV_, Dec 20 2012
%Y Cf. A000217, A000384.
%K base,nonn,easy
%O 0,3
%A Luc Stevens (lms022(AT)yahoo.com), Apr 26 2006
%E Corrected (a(11)=300 inserted) by _Harvey P. Dale_, Dec 20 2012