A178767 Values of gcd(Fibonacci(n), Fibonacci(n+3)+2) sorted with no repeats.

1, 2, 3, 4, 5, 7, 13, 36, 47, 68, 89, 123, 233, 644, 843, 1220, 1597, 2207, 4181, 11556, 15127, 21892, 28657, 39603, 75025, 207364, 271443, 392836, 514229, 710647, 1346269, 3720996, 4870847, 7049156, 9227465, 12752043, 24157817, 66770564, 87403803, 126491972

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 26 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A063726, A178766, A134493, A134497, A000045.

Programs

Maple

a:= proc(n) local l, r;
      l:= [1, 2, 3, 4, 5, 7, 13, 36, 47, 68, 89, 123, 233, 644];
      `if`(n<15, l[n], (<<0|1>, <-1|18>> ^iquo(n-3, 6, 'r').
                        <>) [1,1])
    end:
seq(a(n), n=1..40);  # Alois P. Heinz, Dec 29 2010

Mathematica

Take[Union@Table[GCD[Fibonacci[n],Fibonacci[n+3]+2],{n,1000}],60]

Formula

G.f.: (2*x^14 + 3*x^12 + x^11 + 4*x^10 + 7*x^9 + 5*x^7 - 7*x^6 - 5*x^5 - 4*x^4 - 3*x^3 - 2*x^2 - x) / (-x^12 + 18*x^6 - 1). - Alois P. Heinz, Dec 29 2010