

A082602


Number of primes between successive Fibonacci numbers (including possibly the Fibonacci numbers themselves).


1



0, 1, 2, 2, 2, 2, 3, 3, 5, 8, 11, 17, 24, 37, 55, 85, 126, 198, 297, 458, 704, 1088, 1674, 2602, 4029, 6263, 9738, 15187, 23705, 36981, 57909, 90550, 142033, 222855, 349862, 549903, 865019, 1361581, 2145191, 3381318, 5334509, 8419528, 13298631, 21014892
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..44.


EXAMPLE

a(10)=8 because the 10th Fibonacci number is 55, the 11th is 89 and the eight primes between them are 59, 61, 67, 71, 73, 79, 83 and 89.


MATHEMATICA

lst={}; Do[p=0; Do[If[PrimeQ[a], p++ ], {a, Fibonacci[n], Fibonacci[n+1]}]; AppendTo[lst, p], {n, 50}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 23 2009 *)


PROG

(PARI) { a(n)= c=0; forprime(N=fibonacci(n), fibonacci(n+1), c=c+1); return(c); }
(MAGMA) [#PrimesInInterval(Fibonacci(n1), Fibonacci(n)): n in [2..45]]; // Vincenzo Librandi, Jul 13 2017


CROSSREFS

Sequence in context: A321346 A291444 A219795 * A216644 A187758 A171931
Adjacent sequences: A082599 A082600 A082601 * A082603 A082604 A082605


KEYWORD

nonn


AUTHOR

Hauke Worpel (hw1(AT)email.com), May 23 2003


EXTENSIONS

Corrected and extended by Rick L. Shepherd, May 26 2003
a(43)a(44) from Vincenzo Librandi, Jul 13 2017


STATUS

approved



