A117310 Triangular numbers for which the product of the digits is a hexagonal number.

0, 1, 6, 10, 105, 120, 153, 190, 210, 231, 300, 351, 406, 465, 630, 703, 741, 780, 820, 903, 990, 1035, 1081, 1540, 1770, 1830, 2016, 2080, 2701, 2850, 3003, 3081, 3160, 3240, 3403, 3570, 4005, 4095, 4560, 4950, 5050, 5460, 6105, 6670, 6786, 6903, 7021, 7140

Offset

0,3

Comments

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Example

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.

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A000217, A000384.

Sequence in context: A269341 A348650 A201921 * A174322 A359332 A352132

Adjacent sequences: A117307 A117308 A117309 * A117311 A117312 A117313

Keyword

base,nonn,easy

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 26 2006

Extensions

Corrected (a(11)=300 inserted) by Harvey P. Dale, Dec 20 2012

Status

approved