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A007491
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First prime between n^2 and (n+1)^2.
(Formerly M1389)
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28
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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;
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listen;
history;
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OFFSET
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1,1
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COMMENTS
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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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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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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, Landau's Problem.
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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NextPrime[Range[60]^2] (* From Harvey P. Dale, Mar 24 2011 *)
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PROG
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(PARI) vector(100, i, nextprime(i^2))
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CROSSREFS
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Cf. A053000, A053001, A014085.
Sequence in context: A048210 A153222 A023222 * A124850 A156850 A156611
Adjacent sequences: A007488 A007489 A007490 * A007492 A007493 A007494
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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, Robert G. Wilson v, 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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STATUS
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approved
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