A115313 a(n) = gcd(Lucas(n)+1, Fibonacci(n)+1).

2, 2, 1, 4, 6, 1, 2, 2, 7, 4, 10, 1, 18, 2, 13, 4, 94, 1, 34, 2, 123, 4, 178, 1, 322, 2, 233, 4, 1686, 1, 610, 2, 2207, 4, 3194, 1, 5778, 2, 4181, 4, 30254, 1, 10946, 2, 39603, 4, 57314, 1, 103682, 2, 75025, 4, 542886, 1, 196418, 2, 710647, 4, 1028458, 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 = 1, 2, 7, 8, 9, 14, 15, 20, 26, 27, 32, 33, 38, 44, 50, 56, 62, 68, 74, 80, 86, 87, ... - Vincenzo Librandi, Dec 24 2015

Examples

			a(15) = 13 since F(15) + 1 = 13*47 and L(15) + 1 = 3*5*7*13.
		

Crossrefs

Cf. A000032, A000045, A111956, A115311, A115312, 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}]

PARI

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