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A076777 Number of primes between successive Fibonacci numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A276429 A111181 A267419 * A240210 A111123 A261091
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

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Last modified July 20 09:18 EDT 2024. Contains 374445 sequences. (Running on oeis4.)