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URL: https://oeis.org/A117661

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A117661
Heptagonal numbers for which the product of the digits is also a heptagonal number.
1
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
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
KEYWORD
nonn,base
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), Apr 11 2006
EXTENSIONS
More terms from Emeric Deutsch, Apr 16 2006
STATUS
approved