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

0,5

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)

Formula

a(n) = pi(F(n)) = A000720(A000045(n). - 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

Prog

(Sage) [prime_pi(fibonacci(n)) for n in range(0, 43)] # Zerinvary Lajos, Jun 06 2009
(Magma) [0] cat [#PrimesUpTo(Fibonacci(n)): n in [1..42]]; // Vincenzo Librandi, Apr 25 2019
(PARI) a(n) = primepi(fibonacci(n)); \\ Michel Marcus, Apr 25 2019

Crossrefs

Cf. A000045, A000720.

Sequence in context: A017911 A057048 A281094 * A261082 A271487 A211397

Adjacent sequences: A054779 A054780 A054781 * A054783 A054784 A054785

Keyword

nonn

Author

Jeff Burch, May 22 2000

Extensions

More terms from James A. 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

Status

approved