The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A249403 Decimal expansion of the maximum M(7) of the ratio (Sum_{k=1..7} (x(1)*x(2)*...*x(k))^(1/k))/(x(1) + ... + x(7)) taken over x(1), ..., x(7) > 0. 4
 1, 5, 8, 0, 0, 3, 7, 2, 1, 0, 6, 3, 2, 0, 5, 2, 3, 5, 2, 0, 8, 4, 0, 6, 3, 4, 9, 8, 1, 8, 3, 2, 6, 4, 4, 9, 2, 1, 1, 2, 8, 1, 5, 8, 0, 5, 9, 1, 6, 5, 9, 6, 1, 9, 7, 0, 1, 7, 4, 2, 3, 6, 9, 2, 0, 6, 0, 1, 5, 3, 7, 3, 7, 1, 0, 5, 3, 7, 7, 1, 1, 3, 5, 9, 2, 3, 5, 6, 4, 8, 0, 9, 0, 2, 1, 7, 0, 1, 4, 4, 8, 7, 0, 9, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS M(2) = (1+sqrt(2))/2, M(3) = 4/3. M(n) = exp(1) - 2*Pi^2*exp(1)/(log(n))^2 + O(1/(log(n))^3), [de Bruijn, 1963]. REFERENCES N. G. de Bruijn, Carleman's inequality for finite series, Nederl. Akad. Wetensch. Proc. Ser. A 66 = Indag, Math., 25:505-514, 1963. R. Witula, D. Jama, D. Slota, E. Hetmaniok, Finite version of Carleman's and Knopp's inequalities, Zeszyty naukowe Politechniki Slaskiej (Gliwice, Poland) 92 (2010), 93-96. LINKS Table of n, a(n) for n=1..105. Steven R. Finch, Carleman's inequality, 2013. [Cached copy, with permission of the author] Yu-Dong Wu, Zhi-Hua Zhang and Zhi-Gang Wang, The Best Constant for Carleman's Inequality of Finite Type, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, Vol. 24, No. 2, 2008. EXAMPLE 1.5800372106320523520840634981832644921128158059165961970174236920601537371... MATHEMATICA RealDigits[c7/.FindRoot[{1 + x2/2 + x3/3 + x4/4 + x5/5 + x6/6 + x7/7 == c7, x2/2 + x3/3 + x4/4 + x5/5 + x6/6 + x7/7 == c7*x2^2, x3/3 + x4/4 + x5/5 + x6/6 + x7/7 == c7*x3^3/x2^2, x4/4 + x5/5 + x6/6 + x7/7 == c7*x4^4/x3^3, x5/5 + x6/6 + x7/7 == c7*x5^5/x4^4, x6/6 + x7/7 == c7*x6^6/x5^5, x7/7 == c7*x7^7/x6^6}, {{c7, 3/2}, {x2, 1/2}, {x3, 1/2}, {x4, 1/2}, {x5, 1/2}, {x6, 1/2}, {x7, 1/2}}, WorkingPrecision->120], 10, 105][[1]] CROSSREFS Cf. A174968 = M(2), A219245 = M(4), A219246 = M(5), A219336 = M(6). Sequence in context: A090817 A357054 A198875 * A201756 A242674 A154052 Adjacent sequences: A249400 A249401 A249402 * A249404 A249405 A249406 KEYWORD nonn,cons AUTHOR Vaclav Kotesovec, Oct 27 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 11 09:49 EST 2023. Contains 367722 sequences. (Running on oeis4.)