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A052012 Number of primes between successive Lucas numbers.

%I A052012 #29 Jun 10 2024 08:52:18
%S A052012 1,0,1,0,2,2,4,6,9,15,20,31,48,72,110,170,257,400,608,950,1448,2256,
%T A052012 3487,5413,8440,13118,20478,31932,49995,78222,122553,192262,301826,
%U A052012 474039,745772,1173270,1848000,2912623,4593723,7249438,11448047
%N A052012 Number of primes between successive Lucas numbers.
%H A052012 Amiram Eldar, <a href="/A052012/b052012.txt">Table of n, a(n) for n = 1..100</a>
%F A052012 a(n) = pi(L(n + 1) - 1) - pi(L(n)), where pi is the prime counting function (A000720) and L = A000032. - _Wesley Ivan Hurt_, Nov 09 2023
%F A052012 a(n) = A277062(n+1) - A277062(n) - [n+1 in A001606], where [] denotes the Iverson bracket. - _Amiram Eldar_, Jun 10 2024
%e A052012 Between L(7)=29 and L(8)=47 we find the following primes: 31, 37, 41 and 43 hence a(7)=4.
%t A052012 PrimePi[Last[#]-1]-PrimePi[First[#]]&/@Partition[LucasL[ Range[45]],2,1] (* _Harvey P. Dale_, Jun 28 2011 *)
%o A052012 (Haskell)
%o A052012 a052012 n = a052012_list !! (n-1)
%o A052012 a052012_list = c 1 0 $ tail a000204_list where
%o A052012   c x y ls'@(l:ls) | x < l     = c (x+1) (y + a010051 x) ls'
%o A052012                    | otherwise = y : c (x+1) 0 ls
%o A052012 -- _Reinhard Zumkeller_, Dec 18 2011
%Y A052012 Cf. A000032, A000204, A000720, A001606, A005479, A052011, A277062.
%K A052012 nonn,nice
%O A052012 1,5
%A A052012 _Patrick De Geest_, Nov 15 1999