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.
%I A093062 #38 Dec 09 2024 10:10:44
%S A093062 -1,0,2,8,78,214,1556,4108,28518,513972,1345808,24156990,165578670,
%T A093062 433491846,2971210580,53316283380,956722012572,2504730758802,
%U A093062 44945570173074,308061521102198,806515532933562,14472334024479534,99194853094422264,1779979416004150202
%N A093062 a(n) = Fibonacci(prime(n)) - prime(Fibonacci(n)).
%C A093062 Composition of prime( ) and Fibonacci( ) is not commutative. Does a prime p ever divide Fibonacci(prime(p)) - prime(Fibonacci(p))?
%C A093062 Note that a(3) = 2 is the only prime element of the sequence. This is because after 2, all primes are odd; and the Fibonacci number F(n) is even only for n = 3k for some integer k [which relates to the fact that A082115 Fibonacci sequence (mod 3) is periodic with Pisano period 8]. Hence after a(1) = -1, Fibonacci(prime(n)) - prime(Fibonacci(n)) is always the difference of two odd numbers, hence is even. - _Jonathan Vos Post_, Jan 23 2006
%C A093062 Is a(i) ever divisible by i? Answer: yes. The quotient is an integer for i = 4, 28 and 30 through 63. - Dennis S. Kluk (mathemagician(AT)ameritech.net), Aug 16 2006
%H A093062 Chai Wah Wu, <a href="/A093062/b093062.txt">Table of n, a(n) for n = 1..84</a> (terms 1..41 from Harry J. Smith)
%F A093062 a(n) = Fibonacci(prime(n)) - prime(Fibonacci(n)).
%e A093062 a(11) = Fibonacci(prime(11)) - prime(Fibonacci(11)) = 1345808.
%t A093062 For[i=1, i<61, i++, Print[i, " ", Fibonacci[Prime[i]]-Prime[Fibonacci[i]]]]
%t A093062 Table[Fibonacci[Prime[n]]-Prime[Fibonacci[n]],{n,30}] (* _Harvey P. Dale_, Jul 02 2018 *)
%o A093062 (PARI) a(n) = { fibonacci(prime(n)) - prime(fibonacci(n)) } \\ _Harry J. Smith_, Jun 20 2009
%o A093062 (Magma) [Fibonacci(NthPrime(n)) - NthPrime(Fibonacci(n)): n in [1..30]]; // _Vincenzo Librandi_, Apr 10 2020
%Y A093062 Cf. A000040, A000045, A030427.
%Y A093062 Cf. A082115.
%K A093062 easy,sign
%O A093062 1,3
%A A093062 Dennis S. Kluk (mathemagician(AT)ameritech.net), May 08 2004