A178766 Values of gcd(Fibonacci(n), Fibonacci(n+1)+1) sorted with no repeats.

1, 2, 3, 5, 7, 13, 18, 34, 47, 89, 123, 233, 322, 610, 843, 1597, 2207, 4181, 5778, 10946, 15127, 28657, 39603, 75025, 103682, 196418, 271443, 514229, 710647, 1346269, 1860498, 3524578, 4870847, 9227465, 12752043, 24157817, 33385282, 63245986, 87403803

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

Mix terms of A001519 and A005248. Cf. A063726.

Programs

Maple

a:= n-> `if` (n<2, n, (Matrix (4, (i, j)-> if i+1=j then 1 elif i=4 then [-1, 0, 3, 0][j] else 0 fi)^(n-1). <<2, 2, 3, 5>>)[1, 1]): seq (a(n), n=1..40);  # Alois P. Heinz, Dec 28 2010

Mathematica

Take[Union@Table[GCD[Fibonacci[n],Fibonacci[n+1]+1],{n,1000}],60]
GCD[#[[1]],#[[2]]+1]&/@Partition[Fibonacci[Range[100]],2,1]//Union (* Harvey P. Dale, Sep 22 2016 *)

Formula

G.f.: (x^5 + x^4 - 2*x^2 - x)/(-x^4 + 3*x^2 - 1). - Alois P. Heinz, Dec 28 2010