A274433 Products of two distinct tribonacci numbers > 1.

15, 27, 45, 51, 85, 93, 153, 155, 171, 279, 285, 315, 513, 525, 527, 579, 945, 965, 969, 1065, 1737, 1767, 1775, 1785, 1959, 3195, 3255, 3265, 3281, 3603, 5877, 5983, 5985, 6005, 6035, 6627, 10809, 11001, 11005, 11045, 11101, 12189, 19881, 20235, 20243

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 binary products in increasing order are 15, 27,45, 51, 85, ...
		

Crossrefs

Cf. A000213, A274432, A274434.

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 *)