A115314 a(n) = gcd(Lucas(n)+1, Fibonacci(n)-1).

2, 4, 1, 2, 4, 1, 6, 4, 11, 2, 8, 1, 58, 4, 21, 2, 76, 1, 110, 4, 199, 2, 144, 1, 1042, 4, 377, 2, 1364, 1, 1974, 4, 3571, 2, 2584, 1, 18698, 4, 6765, 2, 24476, 1, 35422, 4, 64079, 2, 46368, 1, 335522, 4, 121393, 2, 439204, 1, 635622, 4, 1149851, 2, 832040, 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, 4, 9, 10, 16, 21, 22, 28, 33, 34, 40, 46, 52, 58, 64, 70, 76, 81, 82, 88, 93, 94, ... - Vincenzo Librandi, Dec 24 2015

Examples

			a(15) = 21 = 3*7 since F(15) - 1 = 3*7*29 and L(15) + 1 = 3*5*7*13.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000032, A000045, A111956, A115311, A115312, A115313.

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}]
Module[{nn=60,l,f},l=LucasL[Range[nn]]+1;f=Fibonacci[Range[nn]]-1;GCD@@@ Thread[ {l,f}]] (* Harvey P. Dale, Apr 29 2020 *)

PARI

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