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A274434 Products of three distinct tribonacci numbers > 1. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..42.

EXAMPLE

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,...

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 *)

CROSSREFS

Cf. A000213, A274432, A274433.

Sequence in context: A096593 A050215 A218417 * A325569 A342189 A176313

Adjacent sequences:  A274431 A274432 A274433 * A274435 A274436 A274437

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 22 2016

STATUS

approved

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Last modified September 26 06:16 EDT 2021. Contains 347664 sequences. (Running on oeis4.)