Search: id:A000006
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%I A000006 M0259 N0092
%S A000006 1,1,2,2,3,3,4,4,4,5,5,6,6,6,6,7,7,7,8,8,8,8,9,9,9,10,10,10,10,
%T A000006 10,11,11,11,11,12,12,12,12,12,13,13,13,13,13,14,14,14,14,15,15,
%U A000006 15,15,15,15,16,16,16,16,16,16,16,17,17,17,17,17,18,18,18,18,18
%N A000006 Integer part of square root of n-th prime.
%C A000006 Conjecture: No two successive terms in the sequence differ by more than 
               1. Proof of this would prove the converse of the theorem that every 
               prime is surrounded by two consecutive squares, namely |sqrt(p)|^2 
               and (|sqrt(p)|+1)^2. - Cino Hilliard (hillcino368(AT)gmail.com), 
               Jan 22 2003
%C A000006 Equals the number of squares less than prime(n). Cf. A014689. - Zak Seidov 
               (zakseidov(AT)yahoo.com) Nov 04 2007
%D A000006 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 2.
%D A000006 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000006 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000006 T. D. Noe, <a href="b000006.txt">Table of n, a(n) for n=1..10000</a>
%H A000006 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%t A000006 a[n_] := IntegerPart[Sqrt[Prime[n]]]
%o A000006 (PARI) a(n)=sqrtint(prime(n)); vector(100,n,a(n))
%Y A000006 Sequence in context: A084557 A024417 A060021 this_sequence A061017 A088462 
               A093337
%Y A000006 Adjacent sequences: A000003 A000004 A000005 this_sequence A000007 A000008 
               A000009
%K A000006 nonn,easy,nice
%O A000006 1,3
%A A000006 N. J. A. Sloane (njas(AT)research.att.com).

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