A010470 - OEIS

A010470

Decimal expansion of square root of 13.

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

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OFFSET

1,1

COMMENTS

Continued fraction expansion is 3 followed by {1, 1, 1, 1, 6} repeated. - Harry J. Smith, Jun 02 2009

The convergents to sqrt(13) are given in A041018/A041019. - Wolfdieter Lang, Nov 23 2017

The fundamental algebraic (integer) number in the field Q(sqrt(13)) is (1 + sqrt(13))/2 = A209927. - Wolfdieter Lang, Nov 21 2023

REFERENCES

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.31.4, p. 201.

LINKS

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

Index entries for algebraic numbers, degree 2.

EXAMPLE

3.605551275463989293119221267470495946251296573845246212710453056227166...

MATHEMATICA

RealDigits[N[Sqrt[13], 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2011 *)

PROG

(PARI) default(realprecision, 20080); x=sqrt(13); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010470.txt", n, " ", d)); \\ Harry J. Smith, Jun 02 2009

CROSSREFS

Cf. A010122 (continued fraction), A041018/A041019 (convergents), A248242 (Egyptian fraction), A171983 (Beatty sequence).

Cf. A020770 (reciprocal), A209927, A295330, A344069.

Sequence in context: A141703 A283193 A021739 * A359295 A181916 A077590

Adjacent sequences: A010467 A010468 A010469 * A010471 A010472 A010473

KEYWORD

nonn,easy,cons,changed

AUTHOR

N. J. A. Sloane

STATUS

approved