product (1 - z^n) for z = 1/2. 1 - 2^-1 - 2^-2 + 2^-5 + 2^-7 - ... The exponents are (negative) pentagonal numbers. The binary expansion of .2887... should be interesting. Rich ________________________________________ From: math-fun-bounces@mailman.xmission.com [math-fun-bounces@mailman.xmission.com] On Behalf Of Joerg Arndt [arndt@jjj.de] Sent: Tuesday, April 01, 2008 1:15 AM To: math-fun Subject: Re: [math-fun] Fraction of indivisible numbers * Fred lunnon <fred.lunnon@gmail.com> [Apr 01. 2008 09:31]:
[...]
f(i) = 2^i (1/2) (3/4) (7/8) (15/16) ... ~= 0.288788095087
This number turns up as the probability that a large random binary matrix is nonsingular. I don't know of a closed form for it --- does anybody else?
M(n)=2^(n*(n-1)/2) * prod(i=1,n, 2^i - 1) n=338; 1.0*M(n)/2^(n*n) 0.2887880950866024212788997219292307800889119048406857841 http://www.research.att.com/~njas/sequences/A002884 Whenever you count the OEIS is your friend. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun