A115312 a(n) = gcd(Lucas(n)-1, Fibonacci(n)+1).

2, 2, 3, 2, 2, 1, 14, 2, 5, 2, 18, 1, 26, 2, 47, 2, 34, 1, 246, 2, 89, 2, 322, 1, 466, 2, 843, 2, 610, 1, 4414, 2, 1597, 2, 5778, 1, 8362, 2, 15127, 2, 10946, 1, 79206, 2, 28657, 2, 103682, 1, 150050, 2, 271443, 2, 196418, 1, 1421294, 2, 514229, 2, 1860498, 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, 3, 4, 5, 8, 9, 10, 14, 15, 16, 20, 21, 22, 26, 28, 32, 33, 34, 38, 40, 44, 45, ... - Vincenzo Librandi, Dec 24 2015

350 of the first 1000 terms are primes. - Harvey P. Dale, Mar 25 2020

Examples

			a(15) = 47 since F(15) + 1 =13*47 and L(15) - 1 = 29*47.
		

Links

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

Crossrefs

Cf. A000032, A000045, A111956, A115311, 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}]
GCD[#[[1]]-1,#[[2]]+1]&/@With[{nn=60},Thread[{LucasL[Range[ nn]],Fibonacci[ Range[nn]]}]] (* Harvey P. Dale, Mar 25 2020 *)

PARI

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