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A052011
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Number of primes between successive Fibonacci numbers.
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4
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0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 10, 16, 23, 37, 55, 84, 125, 198, 297, 458, 704, 1087, 1673, 2602, 4029, 6263, 9738, 15186, 23704, 36981, 57909, 90550, 142033, 222855, 349862, 549903, 865019, 1361581, 2145191, 3381318, 5334509, 8419527, 13298630
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| The formula given and the sequence itself must use the same convention on "between" and what to do if one or both fibonacci numbers are themselves prime. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 08 2010]
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FORMULA
| a(n) = PrimePi(F(n+1)) - PrimePi(F(n)) = A000720(A000045(n+1)) - A000720(A000045(n)). [From Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 08 2010]
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EXAMPLE
| Between Fib(9)=34 and Fib(10)=55 we find the following primes: 37, 41, 43, 47 and 53 hence a(9)=5.
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MATHEMATICA
| lst={}; Do[p=0; Do[If[PrimeQ[a], p++ ], {a, Fibonacci[n]+1, Fibonacci[n+1]-1}]; AppendTo[lst, p], {n, 50}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 23 2009]
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PROG
| (Haskell)
a052011 n = a052011_list !! (n-1)
a052011_list = c 0 0 $ drop 2 a000045_list where
c x y fs'@(f:fs) | x < f = c (x+1) (y + a010051 x) fs'
| otherwise = y : c (x+1) 0 fs
-- Reinhard Zumkeller, Dec 18 2011
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CROSSREFS
| Cf. A000040, A052012.
Cf. A010051.
Sequence in context: A116975 A134792 A033068 * A005468 A104622 A033843
Adjacent sequences: A052008 A052009 A052010 * A052012 A052013 A052014
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KEYWORD
| nonn,nice
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AUTHOR
| Patrick De Geest (pdg(AT)worldofnumbers.com), Nov 15 1999.
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