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A374332 a(n) is the numerator of x(n) = (2*x(n-1) + 1/n) mod 1, with x(0) = 0.

%I A374332 #37 Jul 14 2024 15:42:03
%S A374332 0,0,1,1,11,1,7,64,289,1007,44,338,163,3505,8297,44488,27221,823117,
%T A374332 993287,20403983,26327699,27713369,27650353,315868349,2488325579,
%U A374332 6016553239,1399433807,3562923992,9142117861,275160597119,268889538733,3968532770473,114095155444597
%N A374332 a(n) is the numerator of x(n) = (2*x(n-1) + 1/n) mod 1, with x(0) = 0.
%C A374332 A constant alpha, defined as alpha = Sum_{n >= 1} p(n)/(q(n)*b^n), is b-normal if and only if the associated sequence, defined by x(0) = 0 and x(n) = (b*x(n-1) + p(n)/q(n)) mod 1, is equidistributed in the unit interval.
%C A374332 The present sequence gives the numerators of the associated sequence for alpha = log(2) (where b = 2). See Bailey and Borwein (2005), p. 505 (first example of Theorem 3).
%C A374332 Denominators are given by A374333.
%H A374332 Paolo Xausa, <a href="/A374332/b374332.txt">Table of n, a(n) for n = 0..2000</a>
%H A374332 David H. Bailey and Jonathan M. Borwein, <a href="https://www.ams.org/notices/200505/fea-borwein.pdf">Experimental Mathematics: Examples, Methods and Implications</a>, Notices of the American Mathematical Society, May 2005, Vol. 52, No. 5, pp. 502-514.
%H A374332 David H. Bailey and Richard E. Crandall, <a href="https://doi.org/10.1080/10586458.2001.10504441">On the Random Character of Fundamental Constant Expansions</a>, Experimental Mathematics, Vol. 10 (2001), Issue 2, pp. 175-190 (<a href="https://www.davidhbailey.com/dhbpapers/baicran.pdf">preprint draft</a>).
%H A374332 David H. Bailey and Richard E. Crandall, <a href="https://doi.org/10.1080/10586458.2002.10504704">Random Generators and Normal Numbers</a>, Experimental Mathematics, Vol. 11 (2002), Issue 4, pp. 527-546 (<a href="https://www.davidhbailey.com/dhbpapers/bcnormal-em.pdf">preprint draft</a>).
%t A374332 Block[{n = 0}, Numerator[NestList[Mod[2*# + 1/++n, 1] &, 0, 50]]]
%o A374332 (Python)
%o A374332 from fractions import Fraction
%o A374332 from itertools import count, islice
%o A374332 def A374332_gen(): # generator of terms
%o A374332     a = Fraction(0,1)
%o A374332     for n in count(1):
%o A374332         yield a.numerator
%o A374332         a = (2*a+Fraction(1,n)) % 1
%o A374332 A374332_list = list(islice(A374332_gen(),20)) # _Chai Wah Wu_, Jul 13 2024
%o A374332 (PARI) x(n) = if (n==0, 0, 2*x(n-1) + 1/n);
%o A374332 a(n) = numerator(frac(x(n))); \\ _Michel Marcus_, Jul 13 2024
%Y A374332 Cf. A002162, A374333 (denominators), A374334, A374336.
%K A374332 nonn,frac
%O A374332 0,5
%A A374332 _Paolo Xausa_, Jul 06 2024