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A076777 Number of primes between successive Fibonacci numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

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

LINKS

Table of n, a(n) for n=0..40.

FORMULA

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

EXAMPLE

a(10)=8, as there are 8 primes greater A000045(10)=55 and not greater 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

From Michael B. Porter, Nov 24 2009: (Start)

(PARI) A076777(n) = primepi(fibonacci(n+1))-primepi(fibonacci(n))

A076777(n) = sum(i=fibonacci(n)+1, fibonacci(n+1), isprime(i)) (End)

CROSSREFS

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

STATUS

approved

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Last modified July 25 04:48 EDT 2017. Contains 289779 sequences.