A052012 Number of primes between successive Lucas numbers.

1, 0, 1, 0, 2, 2, 4, 6, 9, 15, 20, 31, 48, 72, 110, 170, 257, 400, 608, 950, 1448, 2256, 3487, 5413, 8440, 13118, 20478, 31932, 49995, 78222, 122553, 192262, 301826, 474039, 745772, 1173270, 1848000, 2912623, 4593723, 7249438, 11448047

Offset

1,5

Links

Amiram Eldar, Table of n, a(n) for n = 1..100

Formula

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

a(n) = A277062(n+1) - A277062(n) - [n+1 in A001606], where [] denotes the Iverson bracket. - Amiram Eldar, Jun 10 2024

Example

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

Mathematica

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

Prog

(Haskell)
a052012 n = a052012_list !! (n-1)
a052012_list = c 1 0 $ tail a000204_list where
  c x y ls'@(l:ls) | x < l     = c (x+1) (y + a010051 x) ls'
                   | otherwise = y : c (x+1) 0 ls
-- Reinhard Zumkeller, Dec 18 2011

Crossrefs

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

Sequence in context: A293552 A293546 A366910 * A234961 A018061 A304778

Adjacent sequences: A052009 A052010 A052011 * A052013 A052014 A052015

Keyword

nonn,nice

Author

Patrick De Geest, Nov 15 1999

Status

approved