A248250 -id:A248250

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A010478

Decimal expansion of square root of 22.

+10
7

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Continued fraction expansion is 4 followed by {1, 2, 4, 2, 1, 8} repeated (A010126). - Harry J. Smith, Jun 03 2009

LINKS

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

Index entries for algebraic numbers, degree 2

EXAMPLE

4.690415759823429554565630113544466280588228353411737153605701891017024....

MATHEMATICA

RealDigits[N[Sqrt[22], 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 22 2011 *)

PROG

(PARI) default(realprecision, 20080); x=sqrt(22); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010478.txt", n, " ", d)); \\ Harry J. Smith, Jun 03 2009

CROSSREFS

Cf. A010126 (continued fraction), A248250 (Egyptian fraction), A020779 (reciprocal).

KEYWORD

nonn,cons,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

A010126

Continued fraction for sqrt(22).

+10
3

4, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

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 (0,0,0,0,0,1).

FORMULA

From Amiram Eldar, Nov 12 2023: (Start)

Multiplicative with a(2^e) = 2, a(3^e) = 4, and a(p^e) = 1 for p >= 5.

Dirichlet g.f.: zeta(s) * (1 + 1/2^s) * (1 + 1/3^(s-1)). (End)

EXAMPLE

4.690415759823429554565630113... = 4 + 1/(1 + 1/(2 + 1/(4 + 1/(2 + ...)))). - Harry J. Smith, Jun 03 2009

MATHEMATICA

ContinuedFraction[Sqrt[22], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)

PadRight[{4}, 120, {8, 1, 2, 4, 2, 1}] (* Harvey P. Dale, Jul 02 2019 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 18000); x=contfrac(sqrt(22)); for (n=0, 20000, write("b010126.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 03 2009