A274434 Products of three distinct tribonacci numbers > 1.

135, 255, 459, 465, 765, 837, 855, 1395, 1539, 1575, 1581, 2565, 2635, 2835, 2895, 2907, 4725, 4743, 4845, 5211, 5301, 5325, 5355, 8685, 8721, 8835, 8925, 9585, 9765, 9795, 9843, 15903, 15975, 16065, 16275, 16405, 17631, 17949, 17955, 18015, 18105, 29295

Offset: 1

Author

Clark Kimberling, Jun 22 2016

Keywords

• nonn
• easy

Comments

Are these unique among all products of distinct tribonacci numbers (A000213)? (See A274432.)

Examples

			The tribonacci numbers > 1 are 3,5,9,17,31,57,..., so that the trinary products in increasing order are 135, 255, 459, 465, 765,...
		

Crossrefs

Cf. A000213, A274432, A274433.

Programs

Mathematica

r[1] := 1; r[2] := 1; r[3] = 1; r[n_] := r[n] = r[n - 1] + r[n - 2] + r[n - 3];
s = {1}; z = 60; f = Map[r, Range[z]]; Take[f, 20]
Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}];
Take[s, 2 z]  (* A274432 *)
infQ[n_] := MemberQ[f, n];
ans = Table[#[[Flatten[Position[Map[Apply[Times, #] &, #], s[[n]]]][[1]]]] &[
Rest[Subsets[Map[#[[1]] &, Select[Map[{#, infQ[#]} &, Divisors[s[[n]]]], #[[2]] && #[[1]] > 1 &]]]]], {n, 2, 300}];
Map[Apply[Times, #] &, Select[ans, Length[#] == 2 &]] (* A274433 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 3 &]] (* A274434 *)
(* Peter J. C. Moses, Jun 17 2016 *)