A054782 Number of primes <= the n-th Fibonacci number.

0, 0, 0, 1, 2, 3, 4, 6, 8, 11, 16, 24, 34, 51, 74, 111, 166, 251, 376, 574, 871, 1329, 2033, 3121, 4794, 7396, 11425, 17688, 27426, 42613, 66317, 103298, 161207, 251757, 393790, 616645, 966507, 1516410, 2381429, 3743010, 5888201, 9269519, 14604028

Offset: 0

Author

Jeff Burch, May 22 2000

Keywords

• nonn

Links

• David Baugh, Table of n, a(n) for n = 0..123 (terms n = 0..70 from H. J. Smith, terms n = 71..123 found using Kim Walisch's primecount program)

Crossrefs

Cf. A000045, A000720.

Programs

Magma

[0] cat [#PrimesUpTo(Fibonacci(n)): n in [1..42]]; // Vincenzo Librandi, Apr 25 2019

Maple

with(combinat): with(numtheory): seq(pi(fibonacci(n)), n = 0 .. 42); # Emeric Deutsch, Jun 24 2009

Mathematica

Table[PrimePi[Fibonacci[n]], {n, 0, 50}] (* Vincenzo Librandi, Apr 25 2019 *)

PARI

a(n) = primepi(fibonacci(n)); \\ Michel Marcus, Apr 25 2019

Sage

[prime_pi(fibonacci(n)) for n in range(0, 43)] # Zerinvary Lajos, Jun 06 2009

Formula

a(n) = pi(F(n)) = A000720(A000045(n)). - Vincenzo Librandi, Apr 25 2019

Extensions

More terms from James Sellers, May 23 2000; and N. J. A. Sloane, Nov 07 2000.

Four more terms from Rick L. Shepherd, Dec 06 2004

Three more terms a(40), a(41), a(42) from Harry J. Smith, Dec 16 2008