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Search: id:A060295
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| A060295 |
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Decimal expansion of e^(Pi*sqrt(163)). |
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+0
16
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| 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, 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, 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
(list; cons; graph; listen)
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OFFSET
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18,1
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COMMENT
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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]
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REFERENCES
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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.
C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Oxford University Press, NY, 1966, p. 106.
H. M. Stark, An Introduction to Number Theory. Markham, Chicago, 1970, p. 179.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=18,...,20000
S. Plouffe, exp(pi*sqrt(163)) to 5000 digits
S. Plouffe, exp(Pi*sqrt(163)), the Ramanujan number,to a precision of 2000 digits
C. Radoux, A Formula of Ramanujan(Text in French)
C. Radoux, A Formula of Ramanujan(Continued) (Text in French)
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics
Titus Piezas III Ramanujan's Constant and its Cousins
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EXAMPLE
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The Ramanujan number = 262537412640768743.99999999999925007259719818568887935...
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MATHEMATICA
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RealDigits[ N[ E^(Pi*Sqrt[163]), 110]] [[1]]
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PROGRAM
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(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]
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CROSSREFS
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Cf. A058292, A019297, A102912.
Sequence in context: A057606 A021385 A085193 this_sequence A102912 A064850 A151853
Adjacent sequences: A060292 A060293 A060294 this_sequence A060296 A060297 A060298
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KEYWORD
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nonn,easy,cons
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Mar 24 2001
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