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A082602 Number of primes between successive Fibonacci numbers (including possibly the Fibonacci numbers themselves).

%I A082602 #26 Sep 08 2022 08:45:10
%S A082602 0,1,2,2,2,2,3,3,5,8,11,17,24,37,55,85,126,198,297,458,704,1088,1674,
%T A082602 2602,4029,6263,9738,15187,23705,36981,57909,90550,142033,222855,
%U A082602 349862,549903,865019,1361581,2145191,3381318,5334509,8419528,13298631,21014892
%N A082602 Number of primes between successive Fibonacci numbers (including possibly the Fibonacci numbers themselves).
%H A082602 Amiram Eldar, <a href="/A082602/b082602.txt">Table of n, a(n) for n = 1..122</a> (calculated using the b-file at A054782)
%e A082602 a(10) = 8 because the 10th Fibonacci number is 55, the 11th is 89 and the eight primes between them are 59, 61, 67, 71, 73, 79, 83 and 89.
%t A082602 lst={};Do[p=0;Do[If[PrimeQ[a],p++ ],{a,Fibonacci[n],Fibonacci[n+1]}];AppendTo[lst,p],{n,50}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 23 2009 *)
%o A082602 (PARI) { a(n)= c=0; forprime(N=fibonacci(n),fibonacci(n+1),c=c+1); return(c); }
%o A082602 (Magma) [#PrimesInInterval(Fibonacci(n-1), Fibonacci(n)): n in [2..45]]; // _Vincenzo Librandi_, Jul 13 2017
%Y A082602 Cf. A000045, A054782, A076777.
%Y A082602 Cf. A001605, A005478.
%K A082602 nonn
%O A082602 1,3
%A A082602 Hauke Worpel (hw1(AT)email.com), May 23 2003
%E A082602 Corrected and extended by _Rick L. Shepherd_, May 26 2003
%E A082602 a(43)-a(44) from _Vincenzo Librandi_, Jul 13 2017