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Search: id:A002193
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| A002193 |
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Decimal expansion of square root of 2.
(Formerly M3195 N1291)
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+0
21
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| 1, 4, 1, 4, 2, 1, 3, 5, 6, 2, 3, 7, 3, 0, 9, 5, 0, 4, 8, 8, 0, 1, 6, 8, 8, 7, 2, 4, 2, 0, 9, 6, 9, 8, 0, 7, 8, 5, 6, 9, 6, 7, 1, 8, 7, 5, 3, 7, 6, 9, 4, 8, 0, 7, 3, 1, 7, 6, 6, 7, 9, 7, 3, 7, 9, 9, 0, 7, 3, 2, 4, 7, 8, 4, 6, 2, 1, 0, 7, 0, 3, 8, 8, 5, 0, 3, 8, 7, 5, 3, 4, 3, 2, 7, 6, 4, 1, 5, 7
(list; cons; graph; listen)
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OFFSET
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1,2
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COMMENT
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Sometimes called Pythagoras's constant.
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REFERENCES
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Steven 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.
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LINKS
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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.
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FORMULA
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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
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CROSSREFS
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Cf. A020807.
Cf. A010503, A001790, A005187.
Sequence in context: A097936 A050338 A077088 this_sequence A020807 A055190 A093063
Adjacent sequences: A002190 A002191 A002192 this_sequence A002194 A002195 A002196
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KEYWORD
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nonn,cons
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AUTHOR
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njas
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