A242103 Numbers m such that m^2 - 1 is the product of three distinct Fibonacci numbers > 1.
7, 9, 11, 14, 29, 76, 121, 199, 329, 521, 659, 1364, 3571, 4523, 7307, 9349, 24476, 64079, 167761, 212533, 439204, 1149851, 3010349, 7881196, 20633239, 54018521, 141422324, 370248451, 969323029, 2537720636, 6643838879, 17393796001, 45537549124, 119218851371
Offset: 1
Keywords
Examples
The non-Lucas number 9 is in the sequence because 9^2-1 = 80 = 2*5*8 is the product of three Fibonacci numbers. The Lucas number 11 is in the sequence because 11^2-1 = 120 = 3*5*8 is the product of three Fibonacci numbers.
Programs
-
Maple
with(combinat,fibonacci):with(numtheory):nn:=150:lst:={}:T:=array(1..nn): for n from 1 to nn do: T[n]:=fibonacci(n): od: for p from 1 to nn-1 do: for q from p+1 to nn-1 do: for r from q+1 to nn-1 do: f:=T[p]*T[q]*T[r]+1:x:=sqrt(f): if x=floor(x)and T[p]<>1 then lst:=lst union {x}: else fi: od: od: od: print(lst): -
PARI
v=[];for(i=3,100,for(j=i+1,100,for(k=j+1,100,s=fibonacci(i)*fibonacci(j)*fibonacci(k);if(issquare(s+1),v=concat(sqrtint(s+1),v)))));v=vecsort(v);v \\ Derek Orr, Aug 27 2014
Comments