keyword:cofr - cp's OEIS frontend

A004200 Continued fraction for Sum_{k>=0} 1/3^(2^k).

0, 2, 5, 3, 3, 1, 3, 5, 3, 1, 5, 3, 1, 3, 3, 5, 3, 1, 5, 3, 3, 1, 3, 5, 1, 3, 5, 3, 1, 3, 3, 5, 3, 1, 5, 3, 3, 1, 3, 5, 3, 1, 5, 3, 1, 3, 3, 5, 1, 3, 5, 3, 3, 1, 3, 5, 1, 3, 5, 3, 1, 3, 3, 5, 3, 1, 5, 3, 3, 1, 3, 5, 3, 1, 5, 3, 1, 3, 3, 5, 3, 1, 5, 3, 3, 1, 3, 5, 1, 3, 5, 3, 1, 3, 3, 5, 1, 3, 5, 3, 3, 1, 3, 5, 3

Offset: 0

N. J. A. Sloane

			0.456942562477639661115491826... = 0 + 1/(2 + 1/(5 + 1/(3 + 1/(3 + ...)))).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Harry J. Smith, Table of n, a(n) for n = 0..20000
Jeffrey O. Shallit, Letter to N. J. A. Sloane with attachment, Aug. 1979
Jeffrey O. Shallit, Simple continued fractions for some irrational numbers, J. Number Theory 11 (1979), no. 2, 209-217.
Jeffrey O. Shallit, Simple continued fractions for some irrational numbers, J. Number Theory 11 (1979), no. 2, 209-217.
Jeffrey O. Shallit, Simple Continued Fractions for Some Irrational Numbers II, J. Number Theory 14 (1982), 228-231.

Cf. A007400, A078885 (decimal expansion).

u := 3: v := 7: Buv := [u,1,[0,u-1,u+1]]: for k from 2 to v do n := nops(Buv[3]): Buv := [u,Buv[2]+1,[seq(Buv[3][i],i=1..n-1),Buv[3][n]+1,Buv[3][n]-1,seq(Buv[3][n-i],i=1..n-2)]] od: seq(Buv[3][i],i=1..2^v);# first 2^v terms of A004200 # Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Dec 02 2002

ContinuedFraction[ NSum[1/3^(2^n), {n, 0, Infinity}, WorkingPrecision -> 105], 105] (* Jean-François Alcover, Jul 18 2011 *)

{ allocatemem(932245000); default(realprecision, 20000); x=suminf(n=0, 1/3^(2^n)); x=contfrac(x); for (n=1, 20001, write("b004200.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 10 2009

Recurrence: a(0)=0, a(1)=2, a(2)=5, a(16n+5)=a(16n+12)=a(32n+9)=a(32n+24)=1, a(8n+3)=a(8n+6)=a(16n+4)=a(16n+13)=a(32n+8)=a(32n+25)=3, a(8n+2)=a(8n+7)=5, a(16n)=a(8n), a(16n+1)=a(8n+1). - Ralf Stephan, May 17 2005

Better description and more terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 19 2001

A010121 Continued fraction for sqrt(7).

Original entry on oeis.org

2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4

Offset: 0

N. J. A. Sloane

This is a basic member of a family of 4-periodic multiplicative sequences with two parameters (c1,c2), defined for n >= 1 by a(n)=1 if n is odd, a(n)=c1 if n == 0 (mod 4) and a(n)=c2 if n == 2 (mod 4). Here, (c1,c2)=(4,1).
The Dirichlet generating function is (1+(c2-1)/2^s+(c1-c2)/4^s)*zeta(s).
Other members are A010123 with parameters (6,2), A010127 (8,3), A010130 (10,1), A010131 (10,2), A010132 (10,4), A010137 (12,5), A010146 (14,6), A089146 (4,8), A109008 (4,2), A112132 (7,3). If c1=c2, this reduces to the cases discussed in A040001. - R. J. Mathar, Feb 18 2011

			2.645751311064590590501615753...  = A010465 = 2 + 1/(1 + 1/(1 + 1/(1 + 1/(4 + ...)))).

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.

Harry J. Smith, Table of n, a(n) for n = 0..20000
C. Elsner, Series of Error Terms for Rational Approximations of Irrational Numbers, J. Int. Seq. 14 (2011) # 11.1.4, example 5.
G. Xiao, Contfrac
Index entries for continued fractions for constants
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Cf. A010465 (decimal expansion).

ContinuedFraction[Sqrt[7],300] (* Vladimir Joseph Stephan Orlovsky, Mar 04 2011 *)
CoefficientList[Series[(2 x^2 + 3 x + 2) (x^2 - x + 1) / ((1 - x) (1 + x) (x^2 + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Nov 26 2016 *)
PadRight[{2},120,{4,1,1,1}] (* Harvey P. Dale, Nov 30 2019 *)

{ allocatemem(932245000); default(realprecision, 13000); x=contfrac(sqrt(7)); for (n=0, 20000, write("b010121.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 01 2009

From R. J. Mathar, Jun 17 2009: (Start)
G.f.: -(2*x^2+3*x+2)*(x^2-x+1)/((x-1)*(1+x)*(x^2+1)).
a(n) = a(n-4), n > 4. (End)
a(n) = (7 + 3*(-1)^n + 3*(-i)^n + 3*i^n)/4, n > 0, where i is the imaginary unit. - Bruno Berselli, Feb 18 2011

A041006 Numerators of continued fraction convergents to sqrt(6).

Original entry on oeis.org

2, 5, 22, 49, 218, 485, 2158, 4801, 21362, 47525, 211462, 470449, 2093258, 4656965, 20721118, 46099201, 205117922, 456335045, 2030458102, 4517251249, 20099463098, 44716177445, 198964172878, 442644523201, 1969542265682, 4381729054565, 19496458483942

Offset: 0

N. J. A. Sloane

Interspersion of 2 sequences, 2*A054320 and A001079. - Gerry Martens, Jun 10 2015

Hugo Pfoertner, Table of n, a(n) for n = 0..100
Index entries for linear recurrences with constant coefficients, signature (0,10,0,-1).

Cf. A041007 (denominators).
Cf. A054320, A001079.
Analog for other sqrt(m): A001333 (m=2), A002531 (m=3), A001077 (m=5), A041008 (m=7), A041010 (m=8), A005667 (m=10), A041014 (m=11), ..., A042936 (m=1000).

I:=[2, 5, 22, 49]; [n le 4 select I[n] else 10*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jun 10 2015

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[6],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 16 2011 *)
LinearRecurrence[{0, 10, 0, -1}, {2, 5, 22, 49}, 50] (* Vincenzo Librandi, Jun 10 2015 *)

A41006=contfracpnqn(c=contfrac(sqrt(6)), #c)[1, ][^-1] \\ Discard possibly incorrect last element. NB: a(n)=A41006[n+1]! M. F. Hasler, Nov 01 2019

\\ For correct index & more terms:
A041006(n)={n<#A041006|| A041006=extend(A041006, [2, 10; 4, -1], n\.8); A041006[n+1]}
extend(A, c, N)={for(n=#A+1, #A=Vec(A, N), A[n]=[A[n-i]|i<-c[, 1]]*c[, 2]); A} \\ M. F. Hasler, Nov 01 2019

From M. F. Hasler, Feb 13 2009: (Start)
a(2n) = 2*A142238(2n) = A041038(2n)/2;
a(2n-1) = A142238(2n-1) = A041038(2n-1) = A001079(n). (End)
G.f.: (2 + 5*x + 2*x^2 - x^3)/(1 - 10*x^2 + x^4).
a(n) = ((2 + sqrt(6))^(n+1) + (2 - sqrt(6))^(n+1))/2^(ceiling(n/2) + 1). - Robert FERREOL, Oct 13 2024
E.g.f.: sqrt(2)*sinh(sqrt(2)*x)*(cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x)) + cosh(sqrt(2)*x)*(2*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x)). - Stefano Spezia, Oct 14 2024

More terms from Vincenzo Librandi, Jun 10 2015

A129408 Continued fraction for L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.

Original entry on oeis.org

0, 1, 7, 1, 1, 1, 1, 1, 5, 1, 1, 9, 4, 13, 4, 1, 2, 27, 1, 28, 1, 2, 2, 3, 2, 7, 1, 1, 19, 1, 8, 3, 3, 2, 1, 10, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 35, 1, 2, 91, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 16, 1, 2, 2, 1, 2, 6, 1, 1, 6, 14, 1, 5, 5, 14, 2, 8, 1, 1, 1, 1, 2, 4, 2, 10, 37, 1, 10, 2, 4, 5, 4, 5, 24, 1, 2, 7, 1

Offset: 0

Stuart Clary, Apr 15 2007

Contributed to OEIS on April 15, 2007 -- the 300th anniversary of the birth of Leonhard Euler.

			L(3, chi3) = 0.8840238117500798567430579168710118077... = [0; 1, 7, 1, 1, 1, 1, 1, 5, 1, 1, 9, 4, 13, 4, ...].

Leonhard Euler, "Introductio in Analysin Infinitorum", First Part, Articles 176 and 292

Cf. A129404, A129405, A129406, A129407, A129409, A129410, A129411.

Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665.

nmax = 1000; ContinuedFraction[4 Pi^3/(81 Sqrt[3]), nmax + 1]

chi3(k) = Kronecker(-3, k); chi3(k) is 0, 1, -1 when k reduced modulo 3 is 0, 1, 2, respectively; chi3 is A049347 shifted.
Series: L(3, chi3) = Sum_{k>=1} chi3(k) k^{-3} = 1 - 1/2^3 + 1/4^3 - 1/5^3 + 1/7^3 - 1/8^3 + 1/10^3 - 1/11^3 + ...
Closed form: L(3, chi3) = 4 Pi^3/(81 sqrt(3)).

A002211 Continued fraction for Khintchine's constant.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Incrementally larger terms in the continued fraction for Khintchine's constant: 1, 2, 5, 10, 24, 90, 770, 941, 11759, 54097, 231973, ..., and they occur at 1, 2, 3, 10, 15, 23, 104, 1701, 2445, 18995, 60037, ... - Robert G. Wilson v, Dec 09 2013

			2.685452001065306445309714835... = 2 + 1/(1 + 1/(2 + 1/(5 + 1/(1 + ...))))
[a_0; a_1, a_2, ...] = [2, 1, 2, ...]

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).

T. D. Noe, Table of n, a(n) for n = 0..999
H. Havermann, Simple Continued Fraction Expansion of Khinchin's Constant
D. Shanks and J. W. Wrench, Jr., Khintchine's constant, Amer. Math. Monthly, 66 (1959), 276-279.
J. W. Wrench, Further evaluation of Khintchine's constant, Math. Comp., 14 (1960), 370-371.
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.
G. Xiao, Contfrac
Eric Weisstein's World of Mathematics, Khinchin's Constant Continued Fraction
Index entries for continued fractions for constants

Cf. A002210.

Mathematica
```
ContinuedFraction[Khinchin, 100]
```

More terms from Robert G. Wilson v, Oct 31 2001

A030168 Continued fraction for Copeland-Erdős constant 0.235711... (concatenate primes).

Original entry on oeis.org

0, 4, 4, 8, 16, 18, 5, 1, 1, 1, 1, 7, 1, 1, 6, 2, 9, 58, 1, 3, 4, 2, 2, 1, 1, 2, 1, 4, 39, 4, 4, 5, 2, 1, 1, 87, 16, 1, 2, 1, 2, 1, 1, 3, 1, 8, 1, 3, 1, 1, 6, 1, 13, 27, 1, 1, 3, 1, 41, 1, 2, 1, 1, 19, 1, 1, 1, 1, 3, 1, 1, 484, 1, 4, 1, 19, 3, 6, 8, 1, 5, 1, 17, 9, 2, 3, 5, 25, 1468, 1, 1, 3, 1

Offset: 0

Eric W. Weisstein

			0.23571113171923293137414347... = 0 + 1/(4 + 1/(4 + 1/(8 + 1/(16 + ...))))

M. F. Hasler, Table of n, a(n) for n = 0..5000
G. Xiao, Contfrac
Eric Weisstein's World of Mathematics, Copeland-Erdős Constant
Index entries for continued fractions for constants

Cf. A033308 (decimal expansion), A072754 (numerators of convergents), A072755 (denominators of convergents).

Take[ ContinuedFraction@ FromDigits[{Flatten[ IntegerDigits[ Prime@Range@ 47]], 0}], 95] (* Robert G. Wilson v, Oct 17 2013 *)

s=concat(vector(2000,i,Str(prime(i)))); c=contfrac(eval(s)/10^#s);
c2=contfrac((eval(s)+10^9)/10^#s);
for(i=1,#c, c[i]!=c2[i] & return(Str("Terms may be wrong for n>="i-1));
write("b030168.txt",i-1," ",c[i])) \\ M. F. Hasler, Oct 13 2009

{ default(realprecision, 2100); x=0.0; m=0; forprime (p=2, 4000, n=1+floor(log(p)/log(10)); x=p+x*10^n; m+=n; ); x=contfrac(x/10^m); for (n=1, 2001, write("b030168.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Apr 30 2009

A040012 Continued fraction for sqrt(17).

Original entry on oeis.org

4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset: 0

N. J. A. Sloane

Decimal expansion of 22/45. - Elmo R. Oliveira, Feb 06 2024

			4.123105625617660549821409855... = 4 + 1/(8 + 1/(8 + 1/(8 + 1/(8 + ...)))). - _Harry J. Smith_, Jun 03 2009

Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §4.4 Powers and Roots, p. 144.
James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, Pages 275-276.

Harry J. Smith, Table of n, a(n) for n = 0..20000
G. Xiao, Contfrac.
Index entries for continued fractions for constants.
Index to divisibility sequences.
Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A041024/A041025 (convergents), A010473 (decimal expansion), A248245 (Egyptian fraction).

Cf. A040000.

Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):

ContinuedFraction[Sqrt[17],300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{4},100,8] (* Harvey P. Dale, Jun 22 2015 *)

{ allocatemem(932245000); default(realprecision, 37000); x=contfrac(sqrt(17)); for (n=0, 20000, write("b040012.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 03 2009

a(n) = 4*A040000(n). - Stefano Spezia, May 14 2023
From Elmo R. Oliveira, Feb 06 2024: (Start)
a(n) = 8 for n >= 1.
G.f.: 4*(1+x)/(1-x).
E.g.f.: 8*exp(x) - 4. (End)

A041019 Denominators of continued fraction convergents to sqrt(13).

Original entry on oeis.org

1, 1, 2, 3, 5, 33, 38, 71, 109, 180, 1189, 1369, 2558, 3927, 6485, 42837, 49322, 92159, 141481, 233640, 1543321, 1776961, 3320282, 5097243, 8417525, 55602393, 64019918, 119622311, 183642229, 303264540, 2003229469, 2306494009, 4309723478, 6616217487, 10925940965

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,36,0,0,0,0,1).

Cf. A010122 (continued fraction for sqrt(13)), A041018 (numerators).

Cf. A041047, A041091, A041151, A041227, A041319, A041427 and A041551. - Johannes W. Meijer, Jun 12 2010

I:=[1, 1, 2, 3, 5, 33, 38, 71, 109, 180]; [n le 10 select I[n] else 36*Self(n-5)+Self(n-10): n in [1..50]]; // Vincenzo Librandi, Dec 10 2013

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[13], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 16 2011 *)
CoefficientList[Series[((1 - 2 x + 4 x^2 - 3 x^3 + x^4) (1 + 3 x + 4 x^2 + 2 x^3 + x^4))/(1 - 36 x^5 - x^10), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2013 *)
LinearRecurrence[{0,0,0,0,36,0,0,0,0,1},{1,1,2,3,5,33,38,71,109,180},40] (* Harvey P. Dale, Sep 30 2016 *)

From Johannes W. Meijer, Jun 12 2010: (Start)
a(5*n) = A006190(3*n+1),
a(5*n+1) = (A006190(3*n+2) - A006190(3*n+1))/2,
a(5*n+2) = (A006190(3*n+2) + A006190(3*n+1))/2,
a(5*n+3) = A006190(3*n+2) and a(5*n+4) = A006190(3*n+3)/2. (End)
G.f.: ((1 - 2*x + 4*x^2 - 3*x^3 + x^4)*(1 + 3*x + 4*x^2 + 2*x^3 + x^4))/(1 - 36*x^5 - x^10). - Peter J. C. Moses, Jul 29 2013
a(n) = A010122(n)*a(n-1) + a(n-2), a(0)=1, a(-1)=0. - Paul Weisenhorn, Aug 17 2018

More terms from Vincenzo Librandi, Dec 10 2013

A040021 Continued fraction for sqrt(27).

Original entry on oeis.org

5, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5

Offset: 0

N. J. A. Sloane

			5.1961524227066318805823390... = 5 + 1/(5 + 1/(10 + 1/(5 + 1/(10 + ...)))). - _Harry J. Smith_, Jun 04 2009

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.

Harry J. Smith, Table of n, a(n) for n = 0..20000
G. Xiao, Contfrac
Index entries for continued fractions for constants
Index entries for linear recurrences with constant coefficients, signature (0,1).

Cf. A010482 (Decimal expansion), A010721.

ContinuedFraction(Sqrt(27)); // G. C. Greubel, Feb 16 2018

Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):

ContinuedFraction[Sqrt[27],300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{5},120,{10,5}] (* Harvey P. Dale, Jul 19 2015 *)

{ allocatemem(932245000); default(realprecision, 35000); x=contfrac(sqrt(27)); for (n=0, 20000, write("b040021.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009

G.f.: 5*(1 + x + x^2)/(1 - x^2). - Stefano Spezia, Jul 26 2025

A123932 a(0) = 1, a(n) = 4 for n > 0.

Original entry on oeis.org

1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 0

Philippe Deléham, Nov 28 2006

Continued fraction for sqrt(5)-1.
a(n) = number of permutations of length n+3 having only one ascent such that the first element of the permutation is 3. - Ran Pan, Apr 20 2015
Also, decimal expansion of 13/90. - Bruno Berselli, Apr 24 2015
Column 1 of A327331 and of A327333. - Omar E. Pol, Nov 25 2019

Index entries for linear recurrences with constant coefficients, signature (1).

Essentially the same as A113311, A040002 and A010709.

[4^n mod 12: n in [0..40]]; // Vincenzo Librandi, Apr 23 2015

ContinuedFraction[Sqrt[5] - 1, 120] (* Michael De Vlieger, Apr 20 2015 *)

makelist(if n=0 then 1 else 4, n, 0, 100); /* Bruno Berselli, Apr 24 2015 */

a(n)=(n>=0)+3*(n>0) \\ Jaume Oliver Lafont, Mar 26 2009

[power_mod(4, n, 12) for n in range(0, 84)] # Zerinvary Lajos, Nov 25 2009

G.f.: (1 + 3*x) / (1 - x).
a(n) = 4 - 3*0^n .
a(n) = 4^n mod 12. - Zerinvary Lajos, Nov 25 2009
E.g.f.: 4*exp(x) - 3. - Elmo R. Oliveira, Aug 06 2024

cp's OEIS Frontend

A004200 Continued fraction for Sum_{k>=0} 1/3^(2^k).

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Maple

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A010121 Continued fraction for sqrt(7).

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A041006 Numerators of continued fraction convergents to sqrt(6).

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Magma

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A129408 Continued fraction for L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.

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A002211 Continued fraction for Khintchine's constant.

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A030168 Continued fraction for Copeland-Erdős constant 0.235711... (concatenate primes).

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PARI

A040012 Continued fraction for sqrt(17).

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