A261141 Positive integers n that can be expressed as a product of Jacobsthal numbers (A001045), not necessarily distinct.

1, 3, 5, 9, 11, 15, 21, 25, 27, 33, 43, 45, 55, 63, 75, 81, 85, 99, 105, 121, 125, 129, 135, 165, 171, 189, 215, 225, 231, 243, 255, 275, 297, 315, 341, 363, 375, 387, 405, 425, 441, 473, 495, 513, 525, 567, 605, 625, 645, 675, 683, 693, 729, 765, 825, 855, 891, 903, 935, 945

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

15 is in the sequence because Jacobsthal numbers 3 and 5 multiply to 15.

Maple

N:= 10000: # to get all terms <= N
J:= gfun:-rectoproc({a(n)=a(n-1)+2*a(n-2), a(0)=0, a(1)=1}, a(n), remember):
P:= {1};
for j from 3 to ilog2(N*3+1) do
  x:= J(j);
  P:= `union`(seq(select(`<=`, map(`*`, P, x^k), N), k=0..floor(log[x](N))))
od:
sort(convert(P, list)); # Robert Israel, Nov 19 2015

Mathematica

max = 11; jacobProds = Table[(2^n - (-1)^n)/3, {n, 2, max]; curr = 2; While[jacobProds[[curr]] < 2^max/3, jacobProds = Union[jacobProds, jacobProds[[curr]] * jacobProds]; curr++]; Select[jacobProds, # < 2^max/3 &] (* Alonso del Arte, Nov 18 2015 *)

Crossrefs

Cf. A001045.

Sequence in context: A104635 A210537 A199407 * A283594 A339173 A233764

Adjacent sequences: A261138 A261139 A261140 * A261142 A261143 A261144

Keyword

nonn

Author

Jeffrey Shallit, Nov 18 2015

Status

approved