0,4

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. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.

Harry J. Smith, Table of n, a(n) for n=0,...,12

G. Xiao, Contfrac

Index entries for continued fractions for constants

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, ...

0.592632718201636... = 0 + 1/(1 + 1/(1 + 1/(2 + 1/(5 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 14 2009]

(PARI) { default(realprecision, 2000); Lehmers=0\

.592632718201636197104078604995701469084275407197161071099562608158\

2473523641600085106647842971012570511871834654238696349260297206760\

6827856079871979437487251403403000583692486915538640614660348566823\

4121548456364466428309378049800689911831849656961720121137594706234\

3698651457715202867734217229580516823444477688944508054163206155851\

2323623064379170223520781603669639276342712524885456742628397234194\

8611415554411186566073479238779804346634255316927539229973648634858\

7121833376712533276555297652866612606618578871362294940308903198431\

3907958405478989509947007489250053656329690017664408563598385209478\

3018218689521378489849677057873565373854975935206722986039362075285\

7617751097879568662935191278445393356845487461466799368867183574393\

7379165908437616570415794750776200309560115740427603024939939214964\

1936741717206542969539031755269515358434395672719151901688809817175\

9724906758187355999053854269057589569016230717484797270186090849699\

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]

Cf. A002794, A002795, A002665, A030125, A002065.

Starting with n=2, a(n)/a(n-2) are in A096407.

Cf. A030125 Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 14 2009]

Adjacent sequences: A002662 A002663 A002664 this_sequence A002666 A002667 A002668

Sequence in context: A114793 A027303 A052695 this_sequence A000665 A058882 A000659

nonn,cofr,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from J. O. Shallit.

The first two terms were missing. Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 14 2009