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A004539 Expansion of sqrt(2) in base 2. 8
1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

R. L. Graham and H. O. Pollak, Note on a nonlinear recurrence related to sqrt(2), Mathematics Magazine, Volume 43, Pages 143-145, 1970. Zbl 201.04705.

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

D. Bailey et al., On the binary expansions of algebraic numbers

Richard Isaac, On the simple normality to base 2 of the square root of s, for s not a perfect square.

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

Thomas Stoll, A fancy way to obtain the binary digits of 759250125 sqrt{2}, (2009),  Amer. Math. Monthly, 117 (2010), 611-617.

Eric Weisstein's World of Mathematics, Wolfram's Iteration

Eric Weisstein's World of Mathematics, Pythagoras's Constant

MATHEMATICA

N[Sqrt[2], 200]; RealDigits[%, 2]

PROG

(bc) obase=2 scale=200 sqrt(2)

(Haskell)

a004539 n = a004539_list !! (n-1)

a004539_list = w 2 0 where

   w x r = bit : w (4 * (x - (4 * r + bit) * bit)) (2 * r + bit)

     where bit = head (dropWhile (\b -> (4 * r + b) * b < x) [0..]) - 1

-- Reinhard Zumkeller, Dec 16 2013

CROSSREFS

Cf. A002193 (decimal version), A233836 (run lengths of 0s and 1s).

Sequence in context: A129360 A129372 A169591 * A023960 A129686 A104974

Adjacent sequences:  A004536 A004537 A004538 * A004540 A004541 A004542

KEYWORD

nonn,base,cons

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified July 25 09:40 EDT 2014. Contains 244907 sequences.