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Search: id:A014085
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| A014085 |
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Number of primes between n^2 and (n+1)^2. |
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+0
30
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| 0, 2, 2, 2, 3, 2, 4, 3, 4, 3, 5, 4, 5, 5, 4, 6, 7, 5, 6, 6, 7, 7, 7, 6, 9, 8, 7, 8, 9, 8, 8, 10, 9, 10, 9, 10, 9, 9, 12, 11, 12, 11, 9, 12, 11, 13, 10, 13, 15, 10, 11, 15, 16, 12, 13, 11, 12, 17, 13, 16, 16, 13, 17, 15, 14, 16, 15, 15, 17, 13, 21, 15, 15, 17, 17, 18, 22, 14, 18, 23, 13
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Suggested by Legendre's conjecture (still open) that there is always a prime between n^2 and (n+1)^2.
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REFERENCES
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J. R. Goldman, The Queen of Mathematics, 1998, p. 82.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Legendre's Conjecture
M. Hassani, Counting primes in the interval (n^2, (n+1)^2)
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FORMULA
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a(n) is the number of occurrences of n in A000006 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 17 2003
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EXAMPLE
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a(17)=5 because between 17^2 and 18^2, i.e. 289 and 324 there are 5 primes (which are 293, 307, 311, 313, 317).
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MATHEMATICA
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Table[ct = PrimePi[(k + 1)^2] - PrimePi[k^2], {k, 0, 80}]. - Lei Zhou (lzhou5@emory.edu), Dec 01 2005
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CROSSREFS
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Cf. A053000, A053001, A007491.
Cf. A077766, A077767.
Cf. A000006.
Sequence in context: A126336 A134446 A125749 this_sequence A029210 A035433 A029199
Adjacent sequences: A014082 A014083 A014084 this_sequence A014086 A014087 A014088
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Jonathan Wild (jon(AT)sound.music.mcgill.ca)
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