OFFSET
1,1
COMMENTS
Conjecture: except the numbers 99 and 15075, all the terms belong to A005248 (bisection of Lucas numbers).
The above conjecture holds for the first 1000 terms. - Jens Kruse Andersen, Aug 10 2014
LINKS
Jens Kruse Andersen, Table of n, a(n) for n = 1..1000
FORMULA
Empirical g.f.: x*(9297*x^9-24320*x^8-52*x^7+52*x^3-127*x^2-42*x+47) / (x^2-3*x+1). - Colin Barker, Aug 13 2014
EXAMPLE
99 is in the sequence because 99^2+1 = 9802 = 2*13*377 where 2, 13 and 377 are three Fibonacci numbers, but 99 is not a Lucas number.
15075 is in the sequence because 15075^2+1 = 13*89*196418 where 13, 89 and 196418 are three Fibonacci numbers, but 15075 is not a Lucas number.
MAPLE
with(combinat, fibonacci):with(numtheory):nn:=200: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):
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michel Lagneau, Jul 29 2014
EXTENSIONS
Doubtful link, formula and PARI code deleted by Colin Barker, Jul 31 2014
STATUS
approved