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A076777 Number of primes between successive Fibonacci numbers. 2

%I

%S 0,0,1,1,1,1,2,2,3,5,8,10,17,23,37,55,85,125,198,297,458,704,1088,

%T 1673,2602,4029,6263,9738,15187,23704,36981,57909,90550,142033,222855,

%U 349862,549903,865019,1361581,2145191,3381318

%N Number of primes between successive Fibonacci numbers.

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

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

%e 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.

%p with(combinat): with(numtheory): seq(pi(fibonacci(n+1))-pi(fibonacci(n)),n=0..35); # _Emeric Deutsch_

%t Table[PrimePi[Fibonacci[k+1]]-PrimePi[Fibonacci[k]],{k,50}] (* _Vladimir Joseph Stephan Orlovsky_, Nov 30 2010 *)

%o From _Michael B. Porter_, Nov 24 2009: (Start)

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

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

%K nonn

%O 0,7

%A _Reinhard Zumkeller_, Nov 14 2002

%E More terms from _Emeric Deutsch_, Mar 02 2005

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Last modified October 22 10:24 EDT 2019. Contains 328317 sequences. (Running on oeis4.)