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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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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
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.
Adjacent sequences: A002208 A002209 A002210 this_sequence A002212 A002213 A002214
Sequence in context: A032259 A109851 A011404 this_sequence A132309 A144224 A122881
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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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