%I #5 Jan 02 2023 03:32:44

%S 2,2,9,2,1,7,3,6,9,5,3

%N Decimal expansion of Knopfmacher's limit: Limit_{x -> 1 from below} (1/(1-x)) * Product_{k>=2} (1 - x^m(k)/(k+1)), where m(k) = A060681(k) = k - k/A020639(k).

%C The problem of calculating this limit was proposed by Knopfmacher (1999) and its value was calculated by Lichtblau (2000).

%H Folkmar Bornemann, Dirk Laurie, Stan Wagon, and Jörg Waldvogel, <a href="https://www-m3.ma.tum.de/m3old/bornemann/challengebook/">The SIAM 100-Digit Challenge, A Study in High-Accuracy Numerical Computing</a>, SIAM, Philadelphia, 2004. See <a href="https://www-m3.ma.tum.de/m3old/bornemann/challengebook/AppendixD/AppendixD.pdf">Appendix D</a>, Problem 3, p. 282.

%H Arnold Knopfmacher, <a href="http://forums.wolfram.com/mathgroup/archive/1999/Jan/msg00023.html">A tricky limit</a>, Usenet news group post to comp.soft-sys.math.mathematica, 1999.

%H Daniel Lichtblau, <a href="https://www-m3.ma.tum.de/m3old/bornemann/challengebook/AppendixD/">The evaluation of Knopfmacher's curious limit</a>, Wolfram Research, Inc., Note of August 2000.

%H Daniel Lichtblau, <a href="https://library.wolfram.com/infocenter/Conferences/7519/">Computing Knopfmacher's Limit, or My First Foray into Computational Mathematics, Reprise</a>, Wolfram Research, Inc., 2009.

%e 2.2921736953...

%Y Cf. A020639, A060681.

%K nonn,cons,more

%O 1,1

%A _Amiram Eldar_, Jan 02 2023