A117661 Heptagonal numbers for which the product of the digits is also a heptagonal number.

0, 1, 7, 1782, 9211, 13213, 212722, 252333, 371911, 766459, 3829753, 5743366, 6534297, 6566671, 13336785, 15347493, 15973168, 17831596, 17965381, 19567813, 27335662, 33154947, 37494513, 47539261, 51817693, 78335613, 93657421

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..130

Example

766459 is in the sequence because it is a heptagonal number and the product of its digits (45360) is also a heptagonal number

Maple

a:=proc(n) local hn, hnn: hn:=convert(n*(5*n-3)/2, base, 10): hnn:=product(hn[j], j=1..nops(hn)): if type((3+sqrt(9+40*hnn))/10, integer)=true then n*(5*n-3)/2 else fi end: seq(a(n), n=0..10000); # Emeric Deutsch, Apr 16 2006

Mathematica

Join[{0}, Select[LinearRecurrence[{3, -3, 1}, {0, 1, 7}, 7000], IntegerQ[(3+ Sqrt[ 40*Times@@IntegerDigits[#]+9])/10]&]] (* Harvey P. Dale, Jun 17 2015 *)
Module[{nn=20000, heps}, heps=PolygonalNumber[7, Range[nn]]; Join[{0}, Select[heps, MemberQ[heps, Times@@IntegerDigits[#]]&]]] (* Harvey P. Dale, Nov 22 2024 *)

Crossrefs

Cf. A000566.

Sequence in context: A203697 A001424 A055318 * A206459 A172937 A185407

Adjacent sequences: A117658 A117659 A117660 * A117662 A117663 A117664

Keyword

nonn,base

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 11 2006

Extensions

More terms from Emeric Deutsch, Apr 16 2006

Status

approved