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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• cons

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

Examples

			3.605551275463989293119221267470495946251296573845246212710453056227166...
		

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.

Crossrefs

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

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

Programs

Mathematica

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

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