A153385 Number of primes <= Fibonacci(Fibonacci(n)) = pi(A007570(n)).

0, 0, 0, 0, 1, 3, 8, 51, 1329, 393790, 5670112879, 43416847208976911

Offset: 0

Author

Harry J. Smith, Dec 25 2008

Keywords

• nonn
• more
• hard

Examples

			a(7) = 51 because Fibonacci(7) = 13, Fibonacci(13) = 233 and there are 51 primes <= 233.
		

Links

• Harry J. Smith, XICalc - Extra Precision Integer Calculator [broken link]
• Kim Walisch, Fast C++ prime counting function implementation (primecount).

Crossrefs

Cf. A000045, A000720, A007570, A054782.

Programs

Magma

[0] cat [#PrimesUpTo(Fibonacci(Fibonacci(n))): n in [1..9]]; // Vincenzo Librandi, Aug 02 2015

Mathematica

PrimePi@# & /@ (Fibonacci@Fibonacci@# & /@ Range@10) (* Robert G. Wilson v, Feb 17 2009 *)

XiCalc

Pi(Fib(Fib(n)));

Formula

a(n) = pi(Fibonacci(Fibonacci(n))) = A000720(A007570(n)).

a(n) = A054782(A000045(n)). - Amiram Eldar, Sep 03 2024

Extensions

a(11) calculated using Kim Walisch's primecount and added by Amiram Eldar, Sep 03 2024