1,2

Sometimes called Pythagoras's constant.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, Section 1.1.

M. Gardner, Gardner's Workout, Chapter 2 "The Square Root of 2=1.414213562373095..." pp. 9-19 A. K. Peters MA 2002.

M. F. Jones, 22900D approximations to the square roots of the primes less than 100, Math. Comp., 22 (1968), 234-235.

Uhler, Horace S.; Many-figures approximations to sqrt{2} and distribution of digits in sqrt{2} and 1/sqrt{2}. Proc. Nat. Acad. Sci. U. S. A. 37, (1951). 63-67.

B. Rittaud, Le fabuleux destin de sqrt(2), Le Pommier, Paris 2006.

D. Flannery, The Square Root of 2, Copernicus Books Springer-Praxis Pub. 2006.

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

I. Khavkine, PlanetMath.org, square root of 2 is irrational

R. Nemiroff and J. Bonnell, The Square Root of Two to 1 Million Digits

R. Nemiroff and J. Bonnell, The Square Root of Two to 5 million digits

R. Nemiroff and J. Bonnell, The first 10 million digits of the square root of 2

S. Plouffe, Plouffe's Inverter, The square root of 2 to 10 million digits

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

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics

D. & J. Ensley, Review of "The Square Root of 2" by D. Flannery

H. S. Uhler, Many-Figure Approximations To Sqrt(2), And Distribution Of Digits In Sqrt(2) And 1/Sqrt(2)

C. P. Simoes, Teste de Desempenho Mental.

Sqrt(2) = 14 * sum_{n=0...infinity} (A001790(n)/2^A005187(floor(n/2)) * 10^(-2n-1)) where A001790(n) are numerators in expansion of 1/sqrt(1-x) and the denominators in expansion of 1/sqrt(1-x) are 2^A005187(n). 14 = 2*7, see A010503 (expansion of 1/sqrt(2)). - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Jan 01 2005

Limit(n-->+oo) of (1/n)*(sum(k=1, n, frac(sqrt(1+zeta(k+1))))) = 1/(1+sqrt(2)) - Yalcin Aktar (aktaryalcin(AT)msn.com), Jul 14 2005

sqrt(2)=2+n*A167199(n-1)/A167199(n) as n-->infinity (conjecture). [From Mats Granvik (mats.granvik(AT)abo.fi), Oct 30 2009]

sqrt(2) = 1.41421356237309504880168872420969807856967187537694807317667... [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 21 2009]

RealDigits[N[2^(1/2), 6! ]] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 25 2008]

(PARI) { default(realprecision, 20080); x=sqrt(2); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b002193.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 21 2009]

Contribution from Michael Porter (michael_b_porter(AT)yahoo.com), Oct 20 2009: (Start)

(PARI) r=0; x=2; /* Digit-by-digit method */

for(digits=1, 100, {d=0; while((20*r+d)*d <= x, d++);

d--; /* while loop overshoots correct digit */

print(d); x=100*(x-(20*r+d)*d); r=10*r+d}) (End)

Cf. A020807.

Cf. A010503, A001790, A005187.

Sequence in context: A050338 A077088 A156896 this_sequence A020807 A055190 A155781

Adjacent sequences: A002190 A002191 A002192 this_sequence A002194 A002195 A002196

nonn,cons,new

N. J. A. Sloane (njas(AT)research.att.com).

Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 19 2009