OFFSET
0,2
COMMENTS
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.
The present sequence gives the numerators of the associated sequence (with b = 2) for alpha = Pi. See Bailey and Borwein (2005), p. 505 (second example of Theorem 3). In the same paper, on p. 513, they conjecture that, for n >= 1, y(n) = floor(16*x(n)) = A062964(n+1). See also Bailey and Crandall (2001), p. 176.
Denominators are given by A374335.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..375
David H. Bailey and Jonathan M. Borwein, Experimental Mathematics: Examples, Methods and Implications, Notices of the American Mathematical Society, May 2005, Vol. 52, No. 5, pp. 502-514.
David H. Bailey and Richard E. Crandall, On the Random Character of Fundamental Constant Expansions, Experimental Mathematics, Vol. 10 (2001), Issue 2, pp. 175-190 (preprint draft).
MATHEMATICA
Block[{n = 0}, Numerator[NestList[Mod[16*# + (120*(++n)^2 - 89*n + 16)/(512*n^4 - 1024*n^3 + 712*n^2 - 206*n + 21), 1] &, 0, 20]]]
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Paolo Xausa, Jul 06 2024
STATUS
approved