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%I #19 May 09 2021 07:54:18
%S 1,6,153,231,351,465,741,6786,24531,57291,58311,123753,153181,167331,
%T 278631,325221,372816,613278,783126,1136278,1476621,1511191,1516411,
%U 1783216,2191371,2512161,2676141,9127128,37311841,44731611,51121216,135112141,137141641
%N Triangular numbers for which the product of the digits is a nonzero hexagonal number.
%C This sequence is a subsequence of A117310.
%H Charles R Greathouse IV, <a href="/A185211/b185211.txt">Table of n, a(n) for n = 1..64</a>
%e 51121216 is included because 5*1*1*2*1*2*1*6=120 and 120 is a hexagonal number.
%t nn=20000;Select[With[{hex=Table[n(2n-1),{n,0,nn}]},Select[Accumulate[ Range[ 0,nn]],MemberQ[hex,Times@@ IntegerDigits[#]]&]], DigitCount[ #,10,0]==0&]
%o (PARI) is(n)=if(ispolygonal(n,3),my(v=digits(n),p=prod(i=1,#v,v[i]));p && ispolygonal(p, 6), 0) \\ _Charles R Greathouse IV_, Dec 20 2012
%Y Cf. A000217, A000384, A117310.
%K base,nonn
%O 1,2
%A _Harvey P. Dale_, Dec 20 2012