%I #24 Oct 01 2022 01:11:43
%S 3,8,55,377,17711,121393,5702887,39088169,1836311903,591286729879,
%T 4052739537881,1304969544928657,61305790721611591,420196140727489673,
%U 19740274219868223167,6356306993006846248183,2046711111473984623691759,14028366653498915298923761,4517090495650391871408712937
%N a(n) = Fibonacci(2*prime(n)).
%C 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.
%C As well, extending the notion, one notes that for k == 1 (mod 4), Fibonacci(2^k * prime(n)) == prime(n) (mod 10).
%C 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
%H Robert Israel, <a href="/A308572/b308572.txt">Table of n, a(n) for n = 1..355</a>
%F a(n) = A000045(A100484(n)). - _Michel Marcus_, Jun 08 2019
%e a(4) = 377, because prime(4) = 7, 2*7 = 14, and Fibonacci(14) is 377.
%p f:= n -> combinat:-fibonacci(2*ithprime(n)):
%p map(f, [$1..30]); # _Robert Israel_, Oct 23 2019
%o (PARI) a(n) = fibonacci(2*prime(n)); \\ _Michel Marcus_, Jun 08 2019
%Y Cf. A000045, A100484, A007652, A054452.
%K nonn
%O 1,1
%A _Christopher Hohl_, Jun 08 2019
%E More terms from _Michel Marcus_, Jun 08 2019