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Search: id:A002211
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| A002211 |
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Continued fraction for Khintchine's constant.
(Formerly M0118 N0047)
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+0
9
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| 2, 1, 2, 5, 1, 1, 2, 1, 1, 3, 10, 2, 1, 3, 2, 24, 1, 3, 2, 3, 1, 1, 1, 90, 2, 1, 12, 1, 1, 1, 1, 5, 2, 6, 1, 6, 3, 1, 1, 2, 5, 2, 1, 2, 1, 1, 4, 1, 2, 2, 3, 2, 1, 1, 4, 1, 1, 2, 5, 2, 1, 1, 3, 29, 8, 3, 1, 4, 3, 1, 10, 50, 1, 2, 2, 7, 6, 2, 2, 16, 4, 4, 2, 2, 3, 1, 1, 7, 1, 5, 1, 2, 1, 5, 3, 1
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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D. Shanks, Further evaluation of Khintchine's constant, Math. Comp., 14 (1960), 370-371.
D. Shanks and J. W. Wrench, Jr., Khintchine's constant, Amer. Math. Monthly, 66 (1959), 276-279.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. W. Wrench, Jr. and D. Shanks, Questions concerning Khintchine's constant and the efficient computation of regular continued fractions, Math. Comp., 20 (1966), 444-448.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
H. Havermann, Simple Continued Fraction Expansion of Khinchin's Constant
G. Xiao, Contfrac
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for continued fractions for constants
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EXAMPLE
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2.685452001065306445309714835... = 2 + 1/(1 + 1/(2 + 1/(5 + 1/(1 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 13 2009]
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MATHEMATICA
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ContinuedFraction[ Khinchin, 100]
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PROGRAM
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Contribution from Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 15 2009: (Start)
(PARI) { default(realprecision, 1201); k=2\
.685452001065306445309714835481795693820382293994462953051152345\
5572188595371520028011411749318476979951534659052880900828976777\
1641096305179253348325966838185231542133211949962603932852204481\
9409618068664166428930847788062036073705350103367263357728904990\
4270702723451702625237023545810686318501032374655803775026442524\
8528694682341899491573066189872079941372355000579357366989339508\
7902124464207528974145914769301844905060179349938522547040420337\
7985639831015709022233910000220772509651332460444439191691460859\
6823482128324622829271012690697418234847767545734898625420339266\
2351862086778136650969658314699527183744805401219536666604964826\
9890827548115254721177330319675947383719393578106059230401890711\
3496246737068412217946810740608918276695667117166837405904739368\
8095345048999704717639045134323237715103219651503824698888324870\
9353994696082647818120566349467125784366645797409778483662049777\
7486827656970871631929385128993141995186116737926546205635059513\
8571376169712687229980532767327871051376395637190231452890030581\
3691090479967275757138504356505064159082099962340277905383418098\
5121278529455415101923273972716796875156245586879771758718269365\
9554502513041968186509380313038584352986863635162; x=contfrac(k); for (n=1, 1257, write("b002211.txt", n, " ", x[n])); } (End)
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CROSSREFS
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Cf. A002210.
Sequence in context: A032259 A109851 A011404 this_sequence A132309 A144224 A122881
Adjacent sequences: A002208 A002209 A002210 this_sequence A002212 A002213 A002214
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KEYWORD
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cofr,nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 31 2001
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