OFFSET
1,1
COMMENTS
Conjecture : except the numbers 9, 14, 121, 329, 659, 4523, 7307 and 212533, a(n) is a Lucas number (A000204).
EXAMPLE
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.
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):
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Aug 15 2014
STATUS
approved