Search: id:A060295
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%I A060295
%S A060295 2,6,2,5,3,7,4,1,2,6,4,0,7,6,8,7,4,3,9,9,9,9,9,9,9,9,9,9,9,9,2,5,0,0,7,
%T A060295 2,5,9,7,1,9,8,1,8,5,6,8,8,8,7,9,3,5,3,8,5,6,3,3,7,3,3,6,9,9,0,8,6,2,7,
%U A060295 0,7,5,3,7,4,1,0,3,7,8,2,1,0,6,4,7,9,1,0,1,1,8,6,0,7,3,1,2,9,5,1,1,8,1
%N A060295 Decimal expansion of e^(Pi*sqrt(163)).
%C A060295 One could observe that the last four of Class Number 1 expressions in 
               http://www.geocities.com/titus_piezas/Ramanujan_a.htm could be expressed 
               as: exp(Pi*sqrt(19+24*n) =~ (24*k)^3 + 31*24 1) n=0 , k= 4 2) n=1 
               , k= 40 3) n=2 , k= 220 4) n=6 , k = 26680 n=6 is the case for Ramanujan 
               constant vs its integer counterpart approximation [From Alexander 
               R. Povolotsky (pevnev(AT)juno.com), Jun 23 2009]
%D A060295 J. Blanck, Exact real arithmetic systems: results of competition, pp. 
               389-393 of J. Blanck et al., eds., Computability and Complexity in 
               Analysis (CCA 2000), Lect. Notes Computer Science, Springer-Verlag, 
               2001.
%D A060295 C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, 
               Oxford University Press, NY, 1966, p. 106.
%D A060295 H. M. Stark, An Introduction to Number Theory. Markham, Chicago, 1970, 
               p. 179.
%H A060295 Harry J. Smith, <a href="b060295.txt">Table of n, a(n) for n=18,...,20000</
               a>
%H A060295 S. Plouffe, <a href="http://pi.lacim.uqam.ca/piDATA/ramanujan.txt">exp(pi*sqrt(163)) 
               to 5000 digits</a>
%H A060295 S. Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/
               math/MiscellaneousMathematicalConstants/chap79.html">exp(Pi*sqrt(163)), 
               the Ramanujan number,to a precision of 2000 digits</a>
%H A060295 C. Radoux, <a href="http://translate.google.com/translate?hl=en&sl=fr&u=http:/
               /users.skynet.be/radoux/163.htm">A Formula of Ramanujan(Text in French)</
               a>
%H A060295 C. Radoux, <a href="http://translate.google.com/translate?hl=en&sl=fr&u=http:/
               /users.skynet.be/radoux/163-2.htm">A Formula of Ramanujan(Continued) 
               (Text in French)</a>
%H A060295 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               RamanujanConstant.html">Link to a section of The World of Mathematics</
               a>
%H A060295 Titus Piezas III <a href="http://www.geocities.com/titus_piezas/Ramanujan_a.htm">
               Ramanujan's Constant and its Cousins</a>
%e A060295 The Ramanujan number = 262537412640768743.99999999999925007259719818568887935...
%t A060295 RealDigits[ N[ E^(Pi*Sqrt[163]), 110]] [[1]]
%o A060295 (PARI) { default(realprecision, 20080); x=exp(Pi*sqrt(163))/10^17; for 
               (n=18, 20000, d=floor(x); x=(x-d)*10; write("b060295.txt", n, " ", 
               d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 03 2009]
%Y A060295 Cf. A058292, A019297, A102912.
%Y A060295 Sequence in context: A057606 A021385 A085193 this_sequence A102912 A064850 
               A151853
%Y A060295 Adjacent sequences: A060292 A060293 A060294 this_sequence A060296 A060297 
               A060298
%K A060295 nonn,easy,cons
%O A060295 18,1
%A A060295 Jason Earls (zevi_35711(AT)yahoo.com), Mar 24 2001

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