A185211 Triangular numbers for which the product of the digits is a nonzero hexagonal number.

1, 6, 153, 231, 351, 465, 741, 6786, 24531, 57291, 58311, 123753, 153181, 167331, 278631, 325221, 372816, 613278, 783126, 1136278, 1476621, 1511191, 1516411, 1783216, 2191371, 2512161, 2676141, 9127128, 37311841, 44731611, 51121216, 135112141, 137141641

Offset

1,2

Comments

This sequence is a subsequence of A117310.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..64

Example

51121216 is included because 5*1*1*2*1*2*1*6=120 and 120 is a hexagonal number.

Mathematica

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&]

Prog

(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

Crossrefs

Cf. A000217, A000384, A117310.

Sequence in context: A221689 A354752 A319036 * A046182 A092122 A285368

Adjacent sequences: A185208 A185209 A185210 * A185212 A185213 A185214

Keyword

base,nonn

Author

Harvey P. Dale, Dec 20 2012

Status

approved