A272950 Products of four distinct Fibonacci numbers > 1.

240, 390, 624, 630, 1008, 1020, 1040, 1560, 1632, 1638, 1650, 1680, 2520, 2640, 2652, 2670, 2720, 2730, 4080, 4095, 4272, 4284, 4290, 4320, 4368, 4400, 4420, 6552, 6600, 6630, 6912, 6930, 6942, 6990, 7072, 7120, 7140, 7150, 10608, 10680, 10710, 10725, 10920

Offset: 1

Author

Clark Kimberling, May 14 2016

Keywords

• nonn
• easy

Examples

			a(1) = 240 = 2*3*5*8.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A160009, A272947, A271354, A272949.

Programs

Mathematica

s = {1}; nn = 60; f = Fibonacci[2 + Range[nn]]; Do[s = Union[s, Select[s*f[[i]], # <= f[[nn]] &]], {i, nn}]; s =  Prepend[s, 0]; Take[s, 100]  (* A160009 *)
isFibonacciQ[n_] := Apply[Or, Map[IntegerQ, Sqrt[{# + 4, # - 4} &[5 n^2]]]];
ans = Join[{{0}}, {{1}}, Table[#[[Flatten[Position[Map[Apply[Times, #] &, #], s[[n]]]][[1]]]] &[Rest[Subsets[Rest[Map[#[[1]] &, Select[Map[{#, isFibonacciQ[#]} &, Divisors[s[[n]]]], #[[2]] &]]]]]], {n, 3, 500}]]
Map[Length, ans] (* A272947 *)
Flatten[Position[Map[Length, ans], 1]]  (* A272948 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 1 &]]  (* A000045 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 2 &]]  (* A271354 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 3 &]]  (* A272949 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 4 &]]  (* A272950 *)
(* Peter J. C. Moses, May 11 2016 *)
up=10^6; F=Fibonacci; i=3; Union[ Reap[ While[(a = F[i++]) < up, j=i; While[ (b = F[j++]*a) < up, h=j; While[(c = F[h++]*b) < up, k=h; While[ (d = F[k++]*c) < up, Sow@d ]]]]][[2, 1]]] (* Giovanni Resta, May 14 2016 *)

PARI

list(lim)=my(v=List(),F,best=5,t2,t3,t4,j,k,l); while(fibonacci(best++)<=30*lim,); F=vector(best,i,fibonacci(i)); for(i=6,best, j=4; while(j++Charles R Greathouse IV, May 14 2016