Search: id:A007491
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%I A007491 M1389
%S A007491 2,5,11,17,29,37,53,67,83,101,127,149,173,197,227,257,293,331,367,401,
%T A007491 443,487,541,577,631,677,733,787,853,907,967,1031,1091,1163,1229,1297,
%U A007491 1373,1447,1523,1601,1693,1777,1861,1949,2027,2129,2213,2309,2411,2503
%N A007491 First prime between n^2 and (n+1)^2.
%C A007491 Alternatively, smallest prime > n^2.
%C A007491 Suggested by Legendre's conjecture (still open) that there is always 
               a prime between n^2 and (n+1)^2.
%D A007491 Archimedeans Problems Drive, Eureka, 24 (1961), 20.
%D A007491 J. R. Goldman, The Queen of Mathematics, 1998, p. 82.
%D A007491 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 
               3rd ed., Oxford Univ. Press, 1954, p. 19.
%D A007491 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007491 T. D. Noe, <a href="b007491.txt">Table of n, a(n) for n=1..1000</a>
%H A007491 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LandausProblems.html">Link to a section of The World of Mathematics.</
               a>
%H A007491 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LegendresConjecture.html">Legendre's Conjecture</a>
%p A007491 [seq(nextprime(i^2), i=1..100)];
%t A007491 Prime[PrimePi[n^2]+1]
%o A007491 (PARI) vector(100,i,nextprime(i^2))
%Y A007491 Cf. A053000, A053001, A014085.
%Y A007491 Sequence in context: A038390 A048210 A023222 this_sequence A124850 A156850 
               A156611
%Y A007491 Adjacent sequences: A007488 A007489 A007490 this_sequence A007492 A007493 
               A007494
%K A007491 nonn,easy,nice
%O A007491 1,1
%A A007491 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com), 
               R. K. Guy
%E A007491 More terms from Labos E. (labos(AT)ana.sote.hu), Nov 17 2000

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