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A093062 a(n) = Fibonacci(prime(n)) - prime(Fibonacci(n)). 3
-1, 0, 2, 8, 78, 214, 1556, 4108, 28518, 513972, 1345808, 24156990, 165578670, 433491846, 2971210580, 53316283380, 956722012572, 2504730758802, 44945570173074, 308061521102198, 806515532933562, 14472334024479534, 99194853094422264, 1779979416004150202 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Composition of prime( ) and Fibonacci( ) is not commutative. Does a prime p ever divide Fibonacci(prime(p)) - prime(Fibonacci(p))?

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

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

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..84 (terms 1..41 from Harry J. Smith)

FORMULA

a(n) = Fibonacci(prime(n)) - prime(Fibonacci(n)).

EXAMPLE

a(11) = Fibonacci(prime(11)) - prime(Fibonacci(11)) = 1345808.

MATHEMATICA

For[i=1, i<61, i++, Print[i, " ", Fibonacci[Prime[i]]-Prime[Fibonacci[i]]]]

Table[Fibonacci[Prime[n]]-Prime[Fibonacci[n]], {n, 30}] (* Harvey P. Dale, Jul 02 2018 *)

PROG

(PARI) { default(primelimit, 4294965247); for(n=1, 41, a=fibonacci(prime(n)) - prime(fibonacci(n)); write("b093062.txt", n, " ", a); ); } \\ Harry J. Smith, Jun 20 2009

(MAGMA) [Fibonacci(NthPrime(n)) - NthPrime(Fibonacci(n)): n in [1..30]]; // Vincenzo Librandi, Apr 10 2020

CROSSREFS

Cf. A000040, A000045, A030427.

Cf. A082115.

Sequence in context: A303943 A295345 A329968 * A057984 A215741 A071254

Adjacent sequences:  A093059 A093060 A093061 * A093063 A093064 A093065

KEYWORD

easy,sign

AUTHOR

Dennis S. Kluk (mathemagician(AT)ameritech.net), May 08 2004

STATUS

approved

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Last modified September 28 19:16 EDT 2021. Contains 347717 sequences. (Running on oeis4.)