A308572 a(n) = Fibonacci(2*prime(n)).

3, 8, 55, 377, 17711, 121393, 5702887, 39088169, 1836311903, 591286729879, 4052739537881, 1304969544928657, 61305790721611591, 420196140727489673, 19740274219868223167, 6356306993006846248183, 2046711111473984623691759, 14028366653498915298923761, 4517090495650391871408712937

Offset: 1

Author

Christopher Hohl, Jun 08 2019

Keywords

• nonn

Comments

This sequence is noteworthy in light of the congruence relation shared by a(n) and prime(n). Namely, for n > 2, a(n) == prime(n) (mod 10). That is, the last digit of prime(n) is 'preserved' as the last digit of a(n). See A007652.

As well, extending the notion, one notes that for k == 1 (mod 4), Fibonacci(2^k * prime(n)) == prime(n) (mod 10).

For any prime number p, the Fibonacci number F_(2p) == -(2p/5) (mod p), where -(2p/5) is the Legendre or Jacobi symbol. - Yike Li, Aug 30 2022

Examples

			a(4) = 377, because prime(4) = 7, 2*7 = 14, and Fibonacci(14) is 377.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..355

Crossrefs

Cf. A000045, A100484, A007652, A054452.

Programs

Maple

f:= n -> combinat:-fibonacci(2*ithprime(n)):
map(f, [$1..30]); # Robert Israel, Oct 23 2019

PARI

a(n) = fibonacci(2*prime(n)); \\ Michel Marcus, Jun 08 2019

Formula

a(n) = A000045(A100484(n)). - Michel Marcus, Jun 08 2019

Extensions

More terms from Michel Marcus, Jun 08 2019