%I A093062
%S A093062 1,0,2,8,78,214,1556,4108,28518,513972,1345808,24156990,165578670,433491846,
%T A093062 2971210580,53316283380,956722012572,2504730758802,44945570173074,308061521102198,
%U A093062 806515532933562,14472334024479534,99194853094422264,1779979416004150202
%V A093062 -1,0,2,8,78,214,1556,4108,28518,513972,1345808,24156990,165578670,433491846,
%W A093062 2971210580,53316283380,956722012572,2504730758802,44945570173074,308061521102198,
%X A093062 806515532933562,14472334024479534,99194853094422264,1779979416004150202
%N A093062 Fibonacci[Prime[i]]-Prime[Fibonacci[i]].
%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 A093062(3) = 2 is the only prime element of the sequence. This 
               is because after 2, all primes are even; 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 A093062(1) = -1, Fibonacci[Prime[n]]-Prime[Fibonacci[n]] 
               is always the difference of two odd numbers, hence is even. - Jonathan 
               Vos Post (jvospost3(AT)gmail.com), 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 Harry J. Smith, <a href="b093062.txt">Table of n, a(n) for n=1,...,41</
               a>
%F A093062 a(n) = Fibonacci[Prime[i]]-Prime[Fibonacci[i]]
%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]]]]
%o A093062 (PARI) { default(primelimit, 4294965247); for(n=1, 41, a=fibonacci(prime(n)) 
               - prime(fibonacci(n)); write("b093062.txt", n, " ", a); ); } [From 
               Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 20 2009]
%Y A093062 Cf. A000040, A000045.
%Y A093062 Cf. A082115.
%Y A093062 Sequence in context: A064605 A132039 A002668 this_sequence A057984 A071254 
               A063528
%Y A093062 Adjacent sequences: A093059 A093060 A093061 this_sequence A093063 A093064 
               A093065
%K A093062 easy,sign
%O A093062 1,3
%A A093062 Dennis S. Kluk (mathemagician(AT)ameritech.net), May 08 2004