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A084596
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a(n) is the number of times n is in sequence A014085, i.e. there are exactly a(n) cases where there are exactly n primes between m^2 and (m+1)^2 for m>=0.
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2
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1, 0, 4, 3, 4, 4, 4, 5, 4, 7, 5, 5, 5, 7, 2, 7, 5, 6, 4, 4, 5, 10, 6, 9, 7, 5, 2, 5, 6, 6, 10, 4, 5, 11, 5, 3, 8, 3, 8, 9, 7, 10, 5, 4, 6, 8, 8, 5, 6, 10, 8, 9, 4, 4, 6, 7, 8, 7, 5, 10, 9, 9, 6, 8, 7, 7, 7, 8, 6, 3, 5, 8, 4, 8, 14, 8, 7, 9, 10, 6, 9, 6, 7, 6, 6, 8, 10, 4, 8, 7, 6, 8, 5, 14, 6, 7, 11, 7, 10, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| This sequences uses a finite number of terms of A014085 to conjecture the behavior of all terms of A014085. The first 10000 terms of this sequence were computed using 120000 terms of A014085. Legendre's conjecture is equivalent to a(0) remaining 1 for all terms of A014085. [Comment reworded by T. D. Noe, Sep 04 2008]
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REFERENCES
| P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 143.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..10000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Landau's Problems.
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EXAMPLE
| a(14)=2 because 14 is in sequence A014085 only two times. There are 14 primes between 64^2 and 65^2 as well as between 77^2 and 78^2. These are the only cases with exactly 14 primes.
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CROSSREFS
| Cf. A007491, A014085, A084597.
Sequence in context: A010308 A200625 A156743 * A056641 A010652 A088752
Adjacent sequences: A084593 A084594 A084595 * A084597 A084598 A084599
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KEYWORD
| nonn
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AUTHOR
| Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2003
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