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

1,2

Links

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

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

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').
                        <<l[3+r], l[9+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]

Crossrefs

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

Sequence in context: A275575 A066661 A268199 * A337188 A125707 A039060

Adjacent sequences: A178764 A178765 A178766 * A178768 A178769 A178770

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 26 2010

Status

approved