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A010467 Decimal expansion of square root of 10. 26
3, 1, 6, 2, 2, 7, 7, 6, 6, 0, 1, 6, 8, 3, 7, 9, 3, 3, 1, 9, 9, 8, 8, 9, 3, 5, 4, 4, 4, 3, 2, 7, 1, 8, 5, 3, 3, 7, 1, 9, 5, 5, 5, 1, 3, 9, 3, 2, 5, 2, 1, 6, 8, 2, 6, 8, 5, 7, 5, 0, 4, 8, 5, 2, 7, 9, 2, 5, 9, 4, 4, 3, 8, 6, 3, 9, 2, 3, 8, 2, 2, 1, 3, 4, 4, 2, 4, 8, 1, 0, 8, 3, 7, 9, 3, 0, 0, 2, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Continued fraction expansion is 3 followed by {6} repeated. [From Harry J. Smith, Jun 02 2009]

In 1594, Joseph Scaliger claimed Pi = sqrt(10), but Ludolph van Ceulen immediately knew this to be wrong. - Alonso del Arte, Jan 17 2013

LINKS

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

Jason Kimberley, Index of expansions of sqrt(d) in base b

R. J. Nemiroff & J. Bonnell, The first 1 million digits of square root of 10

R. J. Nemiroff & J. Bonnell, Plouffe's Inverter, The first 1 million digits of square root of 10

J. J. O'Connor and E. F. Robertson, Ludolph Van Ceulen

FORMULA

Sqrt(10).

a(n) = -10*floor(10^(-(3/2) + n)) + floor(10^(-(1/2) + n)) for n > 0. - Mariusz Iwaniuk, Apr 26 2017

EXAMPLE

3.162277660168379331998893544432718533719555139325216826857504852792594...

Sqrt(10) = sqrt(1 + i*sqrt(15)) + sqrt(1 - i*sqrt(15)) = sqrt(1/2 + 2*i*sqrt(5)) + sqrt(1/2 - 2*i*sqrt(5)), where i = sqrt(-1). - Bruno Berselli, Nov 20 2012

MATHEMATICA

RealDigits[N[Sqrt[10], 200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)

PROG

(PARI) { default(realprecision, 20080); x=sqrt(10); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010467.txt", n, " ", d)); } \\ Harry J. Smith, Jun 02 2009

CROSSREFS

Cf. A040006 (continued fraction).

Sequence in context: A055151 A181187 A104573 * A182182 A158823 A184168

Adjacent sequences:  A010464 A010465 A010466 * A010468 A010469 A010470

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 18 13:07 EST 2018. Contains 299322 sequences. (Running on oeis4.)