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%I #40 Nov 28 2024 19:11:45
%S 6,6,1,3,1,7,0,4,9,4,6,9,6,2,2,3,3,5,2,8,9,7,6,5,8,4,6,2,7,4,1,1,8,5,
%T 3,3,2,8,5,4,7,5,2,8,9,8,3,2,9,1,6,3,5,4,9,8,0,9,0,5,6,2,6,2,2,6,6,2,
%U 5,0,3,1,7,4,3,1,2,2,3,0,4,9,4,2,2,6,1,7,4,0,7,8,4,2,8,1,8,7
%N Decimal expansion of the Feller-Tornier constant (1 + A065474)/2.
%C The asymptotic density of numbers with an even number of non-unitary prime divisors (A333634). - _Amiram Eldar_, May 23 2020
%C Named after the Croatian-American mathematician William Feller (1906-1970) and the German mathematician Erhard Tornier (1894-1982). - _Amiram Eldar_, Jun 16 2021
%D Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.4.1, p. 106.
%H Jayadev S. Athreya, Cristian Cobeli, and Alexandru Zaharescu, <a href="https://arxiv.org/abs/2204.03147">Visibility phenomena in hypercubes</a>, arXiv:2204.03147 [math.NT], 2022.
%H Willy Feller and Erhard Tornier, <a href="https://doi.org/10.1007/BF01448890">Mengentheoretische Untersuchung von Eigenschaften der Zahlenreihe</a>, Mathematische Annalen, Vol. 107 (1933), pp. 188-232.
%H Mizan R. Khan and Riaz R. Khan, <a href="https://arxiv.org/abs/2012.11081">To count clean triangles we count on imph(n)</a>, arXiv:2012.11081 [math.CO], 2020. Mentions this constant.
%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Feller-TornierConstant.html">Feller-Tornier Constant</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeProducts.html">Prime Products</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Feller%E2%80%93Tornier_constant">Feller-Tornier constant</a>.
%e 0.661317049469622335289765846274...
%t digits = 98; r[n_] := -2^n; 1/2 + (1/2) Exp[NSum[r[n]*(PrimeZetaP[2*n]/n), {n, 1, Infinity}, NSumTerms -> 1000, WorkingPrecision -> 2 digits ]] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Apr 16 2016 *)
%o (PARI) (1 + prodeulerrat(1 - 2/p^2))/2 \\ _Amiram Eldar_, Mar 17 2021
%Y Cf. A065474, A078080, A333634.
%K cons,nonn
%O 0,1
%A _N. J. A. Sloane_, Nov 19 2001