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A060295
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Decimal expansion of e^(Pi*sqrt(163)).
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17
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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; constant; graph; refs; listen; history; internal format)
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OFFSET
| 18,1
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COMMENTS
| One could observe that the last four of Class Number 1 expressions in T. Piezas Ramanujan Pages 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]
Integers a(n) in the expression (exp(Pi*sqrt(a(n))))/k (where k is either integer 1 or 8 ) which yield values being very close to whole integer value are: a(n) = {19, 25, 43, 58, 67, 163, 232, ...} Their first differences are all dividable by 3 giving after the division {2,6,5,3,32,33,...} [From Alexander R. Povolotsky (pevnev(AT)juno.com), Oct 16 2010]
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REFERENCES
| 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.
Dimitris Vathis, Letter to N. J. A. Sloane, Apr 22 1985.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=18,...,20000
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 2064/2001.
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, Ramanujan Constant
Tito Piezas III The Ramanujan pages, see section 05.
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EXAMPLE
| The Ramanujan number = 262537412640768743.99999999999925007259719818568887935...
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MATHEMATICA
| RealDigits[ N[ E^(Pi*Sqrt[163]), 110]] [[1]]
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PROG
| (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
| Cf. A058292, A019297, A102912.
Sequence in context: A057606 A021385 A085193 * A102912 A064850 A151853
Adjacent sequences: A060292 A060293 A060294 * A060296 A060297 A060298
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KEYWORD
| nonn,easy,cons
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Mar 24 2001
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