cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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