A115311 a(n) = gcd(Lucas(n)-1, Fibonacci(n)-1).

0, 2, 1, 2, 2, 1, 4, 2, 3, 2, 22, 1, 8, 2, 29, 2, 42, 1, 76, 2, 55, 2, 398, 1, 144, 2, 521, 2, 754, 1, 1364, 2, 987, 2, 7142, 1, 2584, 2, 9349, 2, 13530, 1, 24476, 2, 17711, 2, 128158, 1, 46368, 2, 167761, 2, 242786, 1, 439204, 2, 317811, 2, 2299702, 1

Offset: 1

Author

Giovanni Resta, Jan 20 2006

Keywords

• nonn
• easy

Comments

Here Lucas is: Lucas(1)=1, Lucas(2)=3 and, for n>2, Lucas(n) = Lucas(n-1) + Lucas(n-2). See A000032.

a(n) is prime for n = 2, 4, 5, 8, 9, 10, 14, 15, 16, 20, 22, 26, 27, 28, 32, 34, 38, 39, 40, 44, 46, ... - Vincenzo Librandi, Dec 24 2015

Examples

			a(15) = 29 since F(15) - 1 = 3*7*29 and L(15) - 1 = 29*49.
		

Crossrefs

Cf. A000032, A000045, A111956, A115312, A115313, A115314.

Programs

Magma

[Gcd(Lucas(n)-1, Fibonacci(n)-1): n in [1..60]]; // Vincenzo Librandi, Dec 24 2015

Mathematica

lucas[1]=1; lucas[2]=3; lucas[n_]:= lucas[n]= lucas[n-1] + lucas[n-2]; Table[GCD[lucas[i]-1, Fibonacci[i]-1], {i, 60}]
Table[GCD[LucasL[n]-1,Fibonacci[n]-1],{n,60}] (* Harvey P. Dale, Sep 25 2017 *)

PARI

a(n) = gcd(fibonacci(n+1)+fibonacci(n-1)-1,fibonacci(n)-1); \\ Altug Alkan, Dec 24 2015