Harry J. Smith - cp's OEIS frontend

A159767 Continued fraction expansion of A006891.

2, 1, 1, 85, 2, 8, 1, 10, 16, 3, 8, 9, 2, 1, 40, 1, 2, 3, 2, 2, 1, 17, 1, 1, 5, 3, 2, 6, 3, 5, 1, 1, 3, 3, 15, 3, 1, 1, 7, 2, 3, 1, 7, 2, 1, 55, 1, 1, 1, 1, 4, 9, 1, 2, 1, 36, 1, 5, 10, 1, 1, 2, 1, 4, 1, 4, 5, 5, 1, 1, 130, 1, 3, 1, 1, 2, 1, 3, 1, 3, 2, 3, 2, 2, 547, 9, 18, 3, 1, 4, 2, 1, 1, 2, 2, 2, 1, 6, 1

Offset: 0

Harry J. Smith, Apr 21 2009

Feigenbaum bifurcation velocity alpha.

			-alpha = 2.50290787509589282... = 2 + 1/(1 + 1/(1 + 1/(85 + 1/(2 + ...))))

Harry J. Smith, Table of n, a(n) for n = 0..995

(* assign to 'x' the Feigenbaum bifurcation velocity alpha *); ContinuedFraction[ x, 100] (* Robert G. Wilson v, May 31 2009 *)

{ default(realprecision,1019); alpha=-2.\
5029078750958928222839028732182157863812713767271499773361920567\
7923546317959020670329964974643383412959523186999585472394218237\
7785445179272863314993372578112163594879503744781260997380598671\
2397117373289276654044010306698313834600094139322364490657889951\
2205843172507873377463087853424285351988587500042358246918740820\
4281700901714823051821621619413199856066129382742649709844084470\
1008054549677936760888126446406885181552709324007542506497157047\
0475419932831783645332562415378693957125097066387979492654623137\
6745918909813116752434221110130913127837160951158341230841503716\
4997020224681219644081216686527458043026245782561067150138521821\
6449532543349873487413352795815351016583605455763513276501810781\
1948369459574850237398235452625632779475397269902012891516645793\
9420198920248803394051699686551494477396533876979741232354061781\
9896112494095990353128997733611849847377946108428833293833903950\
9008914086351525626803381414669279913310743349705143545201344643\
4264752001621384610729922641994332772918977769053802596851; x=contfrac(-alpha); for (n=1, 996, write("b159767.txt", n-1, " ", x[n])); } (End)

Old PARI program deleted by Harry J. Smith, May 19 2009

A159671 Continued fraction expansion of Landau's constant L.

Original entry on oeis.org

0, 1, 1, 5, 3, 1, 1, 2, 1, 1, 6, 3, 1, 8, 11, 2, 1, 1, 27, 4, 1, 1, 2, 3, 3, 3, 1, 1, 4, 1, 3, 11, 1, 1, 3, 1, 1, 1, 2, 3, 26, 10, 3, 1, 3, 1, 1, 1, 2, 2, 2, 1, 1, 1, 7, 4, 1, 2, 2, 1, 1, 6, 2, 10, 2, 6, 6, 1, 3, 1, 2, 4, 2, 1, 2, 5, 1, 1, 1, 1, 1, 4, 11, 9, 1, 1, 1, 2, 1, 2, 5, 2, 4, 1, 48, 1, 8, 1, 8, 7, 1, 3

Offset: 0

Harry J. Smith, Apr 19 2009

nonn

Terms are computed using the conjectured formula.

			L = 0.543258965342976706952728...= 0 + 1/(1 + 1/(1 + 1/(5 + 1/(3 + ...)))).

Harry J. Smith, Table of n, a(n) for n = 0..1000

{ default(realprecision, 1080); x=contfrac(gamma(1/3)*gamma(5/6)/gamma(1/6)); d=0; for (n=0, 1000, write("b159671.txt", n, " ", x[n+1])); }

It is conjectured that L = 0.5432589653429767... = Gamma(1/3)*Gamma(5/6)/Gamma(1/6).

A159821 Continued fraction for (ePiphi)^2 A131566, where phi = (1 + sqrt(5))/2.

Original entry on oeis.org

190, 1, 12, 2, 2, 1, 12, 2, 10, 2, 1, 16, 1, 226, 2, 1, 2, 1, 2, 2, 1, 1, 9, 3, 7, 1, 1, 1, 2, 1, 1, 1, 6, 2, 2, 494, 1, 1, 60, 194, 2, 1, 2, 1, 4, 1, 1, 7, 1, 4, 7, 1, 1, 1, 5, 4, 2, 5, 2, 1, 4, 4, 1, 7, 1, 16, 4, 1, 1, 4, 2, 1, 5283, 4, 11, 1, 2, 1, 3, 1, 1, 1, 5, 1, 1, 2, 3, 3, 1, 3, 5, 3, 1, 2, 1, 1, 1

Offset: 0

Harry J. Smith, Apr 26 2009

nonn

			(e*Pi*phi)^2 = 190.925523334... = 190 + 1/(1 + 1/(12 + 1/(2 + 1/(2 + ...)))).

Harry J. Smith, Table of n, a(n) for n = 0..20000

ContinuedFraction[(E*Pi*GoldenRatio)^2,100] (* Harvey P. Dale, Jan 15 2015 *)

{ allocatemem(932245000); default(realprecision, 21000); phi = (1 + sqrt(5))/2; x=contfrac((exp(1)*Pi*phi)^2); for (n=1, 20001, write("b159821.txt", n-1, " ", x[n])); }

A159824 Continued fraction for Pi^Pi (cf. A073233).

Original entry on oeis.org

36, 2, 6, 9, 2, 1, 2, 5, 1, 1, 6, 2, 1, 291, 1, 38, 50, 1, 2, 5, 4, 1, 2, 2, 1, 5, 1, 4, 13, 2, 1, 4, 3, 3, 1, 2, 25, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 3, 1, 43, 1, 2, 7, 3, 1, 1, 1, 2, 4, 2, 1, 1, 3, 1, 3, 3, 2, 2, 16, 3, 5, 2, 1, 5, 2, 1, 10, 1, 1, 3, 1, 13, 1, 1, 3, 1, 10, 4, 1, 1, 1, 38, 1, 2, 2, 1, 1, 3

Offset: 0

Harry J. Smith, Apr 30 2009

nonn

			36.4621596072079117709908260... = 36 + 1/(2 + 1/(6 + 1/(9 + 1/(2 + ...)))).

Harry J. Smith, Table of n, a(n) for n = 0..20000

Cf. A001076, A001203, A001204, A002945, A010767, A011002, A011003, A073233, A073238, A179613, A179615, A179616, A179617.

ContinuedFraction[Pi^Pi,200] (* Vladimir Joseph Stephan Orlovsky, Jul 20 2010 *)

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi^Pi); for (n=1, 20001, write("b159824.txt", n-1, " ", x[n])); }

Edited by N. J. A. Sloane, Jul 22 2010

A160045 Continued fraction for Pi^Pi^Pi A073234.

Original entry on oeis.org

1340164183006357435, 3, 2, 1, 3, 4, 1, 1, 5, 1, 1, 1, 4, 14, 1, 2, 5, 2, 3, 1, 2, 1, 50, 785, 1, 1, 2, 34, 1, 2, 1, 3, 1, 3, 3, 1, 1, 1, 2, 2, 5, 3, 9, 1, 1, 1, 1, 1, 1, 8, 13, 2, 11, 444, 3, 1, 2, 86, 1, 25, 4, 2, 25, 18, 2, 1, 192, 1, 4, 1, 5, 3, 14, 4, 15, 2, 3, 8, 4, 2, 36, 1, 1, 2, 1, 1, 1, 1

Offset: 0

Harry J. Smith, May 01 2009

nonn

Pi^Pi^Pi = 1340164183006357435.2974491296401314150993749745734992377879...

			Pi^Pi^Pi = 1340164183006357435 + 1/(3 + 1/(2 + 1/(1 + 1/(3 + ...)))).

Harry J. Smith, Table of n, a(n) for n = 0..20000

Cf. A073234 Decimal expansion of Pi^Pi^Pi.

ContinuedFraction[Pi^Pi^Pi,90] (* Harvey P. Dale, Sep 10 2014 *)

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi^Pi^Pi); for (n=1, 20001, write("b160045.txt", n-1, " ", x[n])); }

A160331 Decimal expansion of 2^(1/3) + sqrt(3).

Original entry on oeis.org

2, 9, 9, 1, 9, 7, 1, 8, 5, 7, 4, 6, 3, 7, 5, 0, 4, 5, 8, 2, 9, 4, 6, 5, 6, 9, 4, 8, 7, 8, 4, 1, 0, 0, 7, 1, 7, 5, 1, 3, 0, 5, 6, 7, 1, 8, 5, 1, 1, 8, 8, 8, 6, 0, 8, 1, 3, 7, 7, 8, 2, 0, 9, 1, 6, 0, 7, 2, 3, 2, 6, 9, 3, 4, 2, 2, 7, 5, 9, 5, 2, 0, 8, 1, 0, 5, 4, 2, 7, 4, 9, 1, 9, 3, 5, 0, 3, 6, 6, 9, 8, 2, 9, 9, 3

Offset: 1

Harry J. Smith, May 09 2009

2^(1/3) + sqrt(3) = 2^(1/3) + 3^(1/2).

			2.99197185746375045829465694878410071751305671851188860813778209160723...

Harry J. Smith, Table of n, a(n) for n = 1..20000

Cf. A039923 Continued fraction.

RealDigits[Surd[2,3]+Sqrt[3],10,120][[1]] (* Harvey P. Dale, Jan 18 2013 *)

{ default(realprecision, 20080); x=2^(1/3)+3^(1/2); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b160331.txt", n, " ", d)); }

Fixed my PARI program, had -n Harry J. Smith, May 19 2009

A160387 Decimal expansion of 4^5 * Sum_{n>=0} 1/4^(2^n).

Original entry on oeis.org

3, 2, 4, 0, 1, 5, 6, 2, 5, 2, 3, 8, 4, 1, 8, 5, 7, 9, 1, 5, 7, 0, 7, 3, 6, 5, 1, 2, 3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 4, 1, 9, 0, 8, 4, 8, 9, 4, 2, 6, 4, 6, 0, 7, 1, 6, 4, 5, 3, 9, 9, 9, 6, 5, 5, 3, 5, 2, 8, 8, 9, 4, 8, 9, 3, 5, 2, 2, 4, 6, 2, 7, 2, 6, 1, 9, 3, 6, 9, 6, 0, 7, 6, 6, 3, 5, 8, 7, 9, 9, 9, 9, 2, 3, 8, 0

Offset: 3

Harry J. Smith, May 12 2009

			324.0156252384185791570736512312578270241908489426460716453999655352889...

Harry J. Smith, Table of n, a(n) for n = 3..20000

Cf. A006465 Continued fraction.

{ default(realprecision, 20080); x=4^5*suminf(n=0, 1/4^(2^n))/100; for (n=3, 20000, d=floor(x); x=(x-d)*10; write("b160387.txt", n, " ", d)); }

Fixed my PARI program, had -n Harry J. Smith, May 19 2009

A161684 Continued fraction for Pi/(2*sqrt(2)).

Original entry on oeis.org

1, 9, 31, 1, 1, 17, 2, 3, 3, 2, 3, 1, 1, 2, 2, 1, 4, 9, 1, 3, 1, 1, 3, 2, 3, 3, 2, 10, 7, 1, 5, 1, 9, 1, 13, 1, 1, 1, 1, 1, 4, 3, 4, 8, 1, 3, 7, 1, 15, 1, 3, 1, 3, 5, 2, 1, 1, 5, 1, 1, 5, 1, 3, 3, 2, 33, 1, 4, 3, 111, 3, 1, 3, 4, 1, 5, 1, 5, 31, 1, 8, 1, 2, 2, 1, 1, 12, 1, 5, 3, 2, 1, 1, 1, 1, 147, 3, 2, 3, 8

Offset: 0

Harry J. Smith, Jun 17 2009

			1.11072073453959156175397024... = 1 + 1/(9 + 1/(31 + 1/(1 + 1/(1 + ...))))

Harry J. Smith, Table of n, a(n) for n = 0..20000

Cf. A093954 Decimal expansion.

ContinuedFraction[Pi/(2Sqrt[2]),100] (* Harvey P. Dale, Oct 22 2011 *)

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi*sqrt(2)/4); for (n=0, 20000, write("b161684.txt", n, " ", x[n+1])); }

A161688 Continued fraction for zeta(1/2) (negated).

Original entry on oeis.org

1, 2, 5, 1, 4, 6, 1, 1, 2, 6, 1, 1, 2, 1, 1, 1, 37, 3, 2, 1, 2, 4, 1, 368, 2, 1, 23, 18, 1, 1, 2, 2, 2, 11, 1, 4, 1, 5, 40, 1, 2, 1, 2, 1, 1, 1, 1, 2, 4, 1, 10, 2, 5, 4, 1, 12, 2, 5, 3, 1, 7, 2, 1, 2, 1, 1, 1, 6, 1, 12, 1, 2, 2, 2, 1, 2, 36, 2, 3, 1, 1, 1, 4, 3, 2, 45, 4, 5, 1, 1, 7, 3, 1, 1, 3, 6, 2, 1, 19

Offset: 0

Harry J. Smith, Jun 29 2009

nonn

			1.460354508809586812889499152... = 1 + 1/(2 + 1/(5 + 1/(1 + 1/(4 + ...))))

Harry J. Smith, Table of n, a(n) for n = 0..5000

Cf. A059750 Decimal expansion.

{ allocatemem(932245000); default(realprecision, 5400); x=contfrac(-zeta(1/2)); for (n=0, 5000, write("b161688.txt", n, " ", x[n+1])); }

A159822 Continued fraction for Pi*e A019609.

Original entry on oeis.org

8, 1, 1, 5, 1, 3, 1, 4, 12, 3, 2, 1, 5, 2, 12, 1, 1, 1, 10, 2, 2, 2, 3, 8, 3, 2, 2, 2, 29, 1, 1, 13, 1, 1, 8, 11, 16, 3, 1, 4, 163, 2, 1, 1, 1, 5, 1, 6, 1, 17, 5, 1, 3, 6, 3, 1, 4, 1, 1, 1, 5, 1, 7, 15, 4, 1, 1, 1, 9, 1, 1, 4, 1, 1, 9, 1, 55, 14, 14, 1, 3, 2, 3, 7, 1, 118, 1, 2, 29, 1, 2, 2, 1, 4, 1, 2, 1

Offset: 0

Harry J. Smith, Apr 27 2009

			Pi*e = 8.53973422267356706546... = 8 + 1/(1 + 1/(1 + 1/(5 + 1/(1 + ...))))

Harry J. Smith, Table of n, a(n) for n = 0..20000

ContinuedFraction[E*Pi,5! ] (* Vladimir Joseph Stephan Orlovsky, Jun 18 2009 *)

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi*exp(1)); for (n=1, 20001, write("b159822.txt", n-1, " ", x[n])); }

cp's OEIS Frontend

User: Harry J. Smith

A159767 Continued fraction expansion of A006891.

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A159671 Continued fraction expansion of Landau's constant L.

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A159821 Continued fraction for (e*Pi*phi)^2 A131566, where phi = (1 + sqrt(5))/2.

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A159824 Continued fraction for Pi^Pi (cf. A073233).

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A160045 Continued fraction for Pi^Pi^Pi A073234.

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A160331 Decimal expansion of 2^(1/3) + sqrt(3).

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A160387 Decimal expansion of 4^5 * Sum_{n>=0} 1/4^(2^n).

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A161684 Continued fraction for Pi/(2*sqrt(2)).

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A159821 Continued fraction for (ePiphi)^2 A131566, where phi = (1 + sqrt(5))/2.