A248250 -id:A248250 - cp's OEIS frontend

A010478 Decimal expansion of square root of 22.

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

Offset: 1

N. J. A. Sloane

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

			4.690415759823429554565630113544466280588228353411737153605701891017024....

Harry J. Smith, Table of n, a(n) for n = 1..20000
Index entries for algebraic numbers, degree 2

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

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

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

A010126 Continued fraction for sqrt(22).

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

			4.690415759823429554565630113... = 4 + 1/(1 + 1/(2 + 1/(4 + 1/(2 + ...)))). - _Harry J. Smith_, Jun 03 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 (0,0,0,0,0,1).

Cf. A041034/A041035 (convergents), A248250 (Egyptian fraction), A010478 (decimal expansion).

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 *)

{ 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

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)
G.f.: (4 + x + 2*x^2 + 4*x^3 + 2*x^4 + x^5 + 4*x^6)/(1 - x^6). - Stefano Spezia, Jul 26 2025

cp's OEIS Frontend

A010478 Decimal expansion of square root of 22.

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