A082602 Number of primes between successive Fibonacci numbers (including possibly the Fibonacci numbers themselves).

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

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..122 (calculated using the b-file at A054782)

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(n-1), Fibonacci(n)): n in [2..45]]; // Vincenzo Librandi, Jul 13 2017

Crossrefs

Cf. A000045, A054782, A076777.

Cf. A001605, A005478.

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