This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A076777 #33 Jan 12 2025 17:36:42
%S A076777 0,0,1,1,1,1,2,2,3,5,8,10,17,23,37,55,85,125,198,297,458,704,1088,
%T A076777 1673,2602,4029,6263,9738,15187,23704,36981,57909,90550,142033,222855,
%U A076777 349862,549903,865019,1361581,2145191,3381318,5334509,8419528,13298630,21014892,33227992
%N A076777 Number of primes between successive Fibonacci numbers inclusive.
%C A076777 a(n) = #{p prime | A000045(n)<p<=A000045(n+1)}.
%H A076777 Amiram Eldar, <a href="/A076777/b076777.txt">Table of n, a(n) for n = 0..122</a> (calculated using the b-file at A054782)
%F A076777 a(n) = A000720(A000045(n+1)) - A000720(A000045(n)).
%e A076777 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.
%p A076777 with(combinat): with(numtheory): seq(pi(fibonacci(n+1))-pi(fibonacci(n)),n=0..35); # _Emeric Deutsch_
%t A076777 Table[PrimePi[Fibonacci[k+1]]-PrimePi[Fibonacci[k]],{k,50}] (* _Vladimir Joseph Stephan Orlovsky_, Nov 30 2010 *)
%o A076777 (PARI) A076777(n) = primepi(fibonacci(n+1))-primepi(fibonacci(n))
%o A076777 A076777(n) = sum(i=fibonacci(n)+1,fibonacci(n+1),isprime(i)) \\ _Michael B. Porter_, Nov 24 2009
%Y A076777 Cf. A000045, A000720, A054782, A082602.
%Y A076777 Cf. A001605, A005478.
%K A076777 nonn
%O A076777 0,7
%A A076777 _Reinhard Zumkeller_, Nov 14 2002
%E A076777 More terms from _Emeric Deutsch_, Mar 02 2005
%E A076777 More terms from _Amiram Eldar_, Oct 07 2021