OFFSET
1,2
COMMENTS
The sequence is closed under multiplication.
Also, if m is in this sequence (i.e., gcd(F(m),m)=m) then F(m) is in this sequence (since gcd(F(F(m)),F(m)) = F(gcd(F(m),m)) = F(m)).
In particular, this sequence includes all terms of geometric progressions 5^k*Fibonacci(5^m) for integers k >= 0 and m >= 0.
LINKS
EXAMPLE
a(1) = Fibonacci(1) = 1,
a(2) = Fibonacci(5) = 5,
a(3)..a(7) = {5^2, 5^3, 5^4, 5^5, 5^6},
a(8) = 75025 = 5^2*3001 = Fibonacci(5^2),
a(9) = 5^7,
a(10) = 375125 = 5^3*3001 = 5*Fibonacci(5^2),
a(11) = 5^8.
MATHEMATICA
Do[ If[ !IntegerQ[ n/12 ] && IntegerQ[ Fibonacci[n] / n ], Print[n] ], {n, 1, 5^8} ]
PROG
(PARI) is(n)=n%12 && (Mod([0, 1; 1, 1], n)^n*[0; 1])[1, 1]==0 \\ Charles R Greathouse IV, Nov 04 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, May 11 2007
EXTENSIONS
Edited and extended by Max Alekseyev, Sep 20 2009
a(1)=1 added by Zak Seidov, Nov 01 2009
Edited and extended by Max Alekseyev, Jan 20 2010
STATUS
approved