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Search: id:A007491
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| A007491 |
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First prime between n^2 and (n+1)^2.
(Formerly M1389)
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+0
20
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| 2, 5, 11, 17, 29, 37, 53, 67, 83, 101, 127, 149, 173, 197, 227, 257, 293, 331, 367, 401, 443, 487, 541, 577, 631, 677, 733, 787, 853, 907, 967, 1031, 1091, 1163, 1229, 1297, 1373, 1447, 1523, 1601, 1693, 1777, 1861, 1949, 2027, 2129, 2213, 2309, 2411, 2503
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Alternatively, smallest prime > n^2.
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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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Archimedeans Problems Drive, Eureka, 24 (1961), 20.
J. R. Goldman, The Queen of Mathematics, 1998, p. 82.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 19.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Legendre's Conjecture
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MAPLE
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[seq(nextprime(i^2), i=1..100)];
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MATHEMATICA
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Prime[PrimePi[n^2]+1]
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PROGRAM
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(PARI) vector(100, i, nextprime(i^2))
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CROSSREFS
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Cf. A053000, A053001, A014085.
Adjacent sequences: A007488 A007489 A007490 this_sequence A007492 A007493 A007494
Sequence in context: A038390 A048210 A023222 this_sequence A124850 A156850 A156611
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com), R. K. Guy
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EXTENSIONS
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More terms from Labos E. (labos(AT)ana.sote.hu), Nov 17 2000
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