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 A088367 Decimal expansion of Krivine's bound for Grothendieck's constant, Pi/(2*log(1+sqrt(2))). 7
 1, 7, 8, 2, 2, 1, 3, 9, 7, 8, 1, 9, 1, 3, 6, 9, 1, 1, 1, 7, 7, 4, 4, 1, 3, 4, 5, 2, 9, 7, 2, 5, 4, 9, 3, 4, 0, 7, 9, 1, 7, 3, 1, 9, 0, 9, 7, 7, 3, 2, 3, 9, 3, 8, 1, 0, 2, 4, 9, 5, 9, 9, 5, 6, 8, 8, 5, 1, 5, 4, 1, 2, 8, 7, 6, 3, 7, 8, 4, 0, 8, 0, 2, 4, 3, 1, 6, 7, 6, 6, 3, 5, 7, 8, 2, 5, 5, 3, 0, 8, 9, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Krivine (1977) proved that Grothendieck's constant <= Pi/(2*log(1+sqrt(2))), and conjectured that this bound is the exact value of the constant. His conjecture was refuted by Braverman et al. (2013). - Amiram Eldar, Jun 24 2021 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 3.11, pp. 235-237. LINKS G. C. Greubel, Table of n, a(n) for n = 1..20000 Noga Alon, Konstantin Makarychev, Yury Makarychev and Assaf Naor, Quadratic forms on graphs, Inventiones Math., Vol. 163 (2006), pp. 499-522; preprint. Mark Braverman, Konstantin Makarychev, Yury Makarychev and Assaf Naor, The Grothendieck constant is strictly smaller than Krivine's bound, Forum of Mathematics, Pi, Vol. 1 (2013), e4. Jean-Louis Krivine, Sur la constante de Grothendieck, C. R. Acad. Sci. Paris, Series A and B, Vol. 284, No. 8 (1977), pp. A445-A446. Simon Plouffe, Grothendieck's majorant. Eric Weisstein's World of Mathematics, Grothendieck's Constant. Wikipedia, Grothendieck inequality. EXAMPLE 1.7822139781913691117744134529725493407917319097732... MATHEMATICA RealDigits[Pi/(2*Log[1 + Sqrt[2]]), 10, 111][[1]] (* Robert G. Wilson v, May 19 2004 *) PROG (PARI) Pi/(2*log(1 + sqrt(2))) \\ G. C. Greubel, Mar 27 2018 (Magma) SetDefaultRealField(RealField(150)); R:= RealField(); Pi(R)/(2*Log(1 + Sqrt(2))) // G. C. Greubel, Mar 27 2018 CROSSREFS Sequence in context: A154169 A245260 A128755 * A196610 A198938 A244067 Adjacent sequences: A088364 A088365 A088366 * A088368 A088369 A088370 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Sep 27 2003 EXTENSIONS Edited by N. J. A. Sloane, Oct 01 2006 Named edited by Amiram Eldar, Jun 24 2021 STATUS approved

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Last modified December 4 10:52 EST 2023. Contains 367560 sequences. (Running on oeis4.)