A052012 - OEIS

%I #29 Jun 10 2024 08:52:18

%S 1,0,1,0,2,2,4,6,9,15,20,31,48,72,110,170,257,400,608,950,1448,2256,

%T 3487,5413,8440,13118,20478,31932,49995,78222,122553,192262,301826,

%U 474039,745772,1173270,1848000,2912623,4593723,7249438,11448047

%N Number of primes between successive Lucas numbers.

%H Amiram Eldar, <a href="/A052012/b052012.txt">Table of n, a(n) for n = 1..100</a>

%F 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 a(n) = A277062(n+1) - A277062(n) - [n+1 in A001606], where [] denotes the Iverson bracket. - _Amiram Eldar_, Jun 10 2024

%e Between L(7)=29 and L(8)=47 we find the following primes: 31, 37, 41 and 43 hence a(7)=4.

%t PrimePi[Last[#]-1]-PrimePi[First[#]]&/@Partition[LucasL[ Range[45]],2,1] (* _Harvey P. Dale_, Jun 28 2011 *)

%o (Haskell)

%o a052012 n = a052012_list !! (n-1)

%o a052012_list = c 1 0 $ tail a000204_list where

%o   c x y ls'@(l:ls) | x < l     = c (x+1) (y + a010051 x) ls'

%o                    | otherwise = y : c (x+1) 0 ls

%o -- _Reinhard Zumkeller_, Dec 18 2011

%Y Cf. A000032, A000204, A000720, A001606, A005479, A052011, A277062.

%K nonn,nice

%O 1,5

%A _Patrick De Geest_, Nov 15 1999