A076777 Number of primes between successive Fibonacci numbers inclusive.

0, 0, 1, 1, 1, 1, 2, 2, 3, 5, 8, 10, 17, 23, 37, 55, 85, 125, 198, 297, 458, 704, 1088, 1673, 2602, 4029, 6263, 9738, 15187, 23704, 36981, 57909, 90550, 142033, 222855, 349862, 549903, 865019, 1361581, 2145191, 3381318, 5334509, 8419528, 13298630, 21014892, 33227992

Offset: 0

Author

Reinhard Zumkeller, Nov 14 2002

Keywords

• nonn

Comments

a(n) = #{p prime | A000045(n)A000045(n+1)}.

Examples

			a(10) = 8, as there are 8 primes greater than A000045(10) = 55 and not greater than A000045(10+1) = 89: 59, 61, 67, 71, 73, 79, 83 and 89.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..122 (calculated using the b-file at A054782)

Crossrefs

Cf. A000045, A000720, A054782, A082602.

Cf. A001605, A005478.

Programs

Maple

with(combinat): with(numtheory): seq(pi(fibonacci(n+1))-pi(fibonacci(n)),n=0..35); # Emeric Deutsch

Mathematica

Table[PrimePi[Fibonacci[k+1]]-PrimePi[Fibonacci[k]],{k,50}] (* Vladimir Joseph Stephan Orlovsky, Nov 30 2010 *)

PARI

A076777(n) = primepi(fibonacci(n+1))-primepi(fibonacci(n))
A076777(n) = sum(i=fibonacci(n)+1,fibonacci(n+1),isprime(i)) \\ Michael B. Porter, Nov 24 2009

Formula

a(n) = A000720(A000045(n+1)) - A000720(A000045(n)).

Extensions

More terms from Emeric Deutsch, Mar 02 2005

More terms from Amiram Eldar, Oct 07 2021