A076777 Number of primes between successive Fibonacci numbers.

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

0,7

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000045, A000720, A054782, A082602.

Cf. A001605, A005478.

Sequence in context: A276429 A111181 A267419 * A240210 A111123 A261091

Adjacent sequences: A076774 A076775 A076776 * A076778 A076779 A076780

Keyword

nonn

Author

Reinhard Zumkeller, Nov 14 2002

Extensions

More terms from Emeric Deutsch, Mar 02 2005

More terms from Amiram Eldar, Oct 07 2021

Status

approved