Search: id:A002665
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%I A002665 M1549 N0605
%S A002665 0,1,1,2,5,34,985,1151138,1116929202845,1480063770341062927127746,
%T A002665 1846425204836010506550936273411258268076151412465
%N A002665 Continued fraction expansion of Lehmer's constant.
%D A002665 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002665 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002665 D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. 
               J., 4 (1935), 323-340.
%H A002665 Harry J. Smith, <a href="b002665.txt">Table of n, a(n) for n=0,...,12</
               a>
%H A002665 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">
               Contfrac</a>
%H A002665 <a href="Sindx_Con.html#confC">Index entries for continued fractions 
               for constants</a>
%F A002665 With a different offset: a(0)=1, a(1)=1, a(n+1)=(b(n)+b(n-1)+1)*a(n-1), 
               n >= 1, b()=A002065, with b(0)=0, b(1)=1, b(2)=3, ...
%e A002665 0.592632718201636... = 0 + 1/(1 + 1/(1 + 1/(2 + 1/(5 + ...)))) [From 
               Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 14 2009]
%o A002665 (PARI) { default(realprecision, 2000); Lehmers=0\
%o A002665 .592632718201636197104078604995701469084275407197161071099562608158\
%o A002665 2473523641600085106647842971012570511871834654238696349260297206760\
%o A002665 6827856079871979437487251403403000583692486915538640614660348566823\
%o A002665 4121548456364466428309378049800689911831849656961720121137594706234\
%o A002665 3698651457715202867734217229580516823444477688944508054163206155851\
%o A002665 2323623064379170223520781603669639276342712524885456742628397234194\
%o A002665 8611415554411186566073479238779804346634255316927539229973648634858\
%o A002665 7121833376712533276555297652866612606618578871362294940308903198431\
%o A002665 3907958405478989509947007489250053656329690017664408563598385209478\
%o A002665 3018218689521378489849677057873565373854975935206722986039362075285\
%o A002665 7617751097879568662935191278445393356845487461466799368867183574393\
%o A002665 7379165908437616570415794750776200309560115740427603024939939214964\
%o A002665 1936741717206542969539031755269515358434395672719151901688809817175\
%o A002665 9724906758187355999053854269057589569016230717484797270186090849699\
%o A002665 968957675960828498381969270404195036511309800972643309599823665; x=contfrac(Lehmers); 
               for (n=1, 13, write("b002665.txt", n-1, " ", x[n])); } [From Harry 
               J. Smith (hjsmithh(AT)sbcglobal.net), May 14 2009]
%Y A002665 Cf. A002794, A002795, A002665, A030125, A002065.
%Y A002665 Starting with n=2, a(n)/a(n-2) are in A096407.
%Y A002665 Cf. A030125 Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 14 2009]
%Y A002665 Sequence in context: A114793 A027303 A052695 this_sequence A000665 A058882 
               A000659
%Y A002665 Adjacent sequences: A002662 A002663 A002664 this_sequence A002666 A002667 
               A002668
%K A002665 nonn,cofr,nice,easy
%O A002665 0,4
%A A002665 N. J. A. Sloane (njas(AT)research.att.com).
%E A002665 More terms from J. O. Shallit.
%E A002665 The first two terms were missing. Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 14 2009

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