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A374332
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a(n) is the numerator of x(n) = (2*x(n-1) + 1/n) mod 1, with x(0) = 0.
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4
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0, 0, 1, 1, 11, 1, 7, 64, 289, 1007, 44, 338, 163, 3505, 8297, 44488, 27221, 823117, 993287, 20403983, 26327699, 27713369, 27650353, 315868349, 2488325579, 6016553239, 1399433807, 3562923992, 9142117861, 275160597119, 268889538733, 3968532770473, 114095155444597
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OFFSET
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0,5
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COMMENTS
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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 for alpha = log(2) (where b = 2). See Bailey and Borwein (2005), p. 505 (first example of Theorem 3).
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LINKS
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MATHEMATICA
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Block[{n = 0}, Numerator[NestList[Mod[2*# + 1/++n, 1] &, 0, 50]]]
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PROG
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(Python)
from fractions import Fraction
from itertools import count, islice
def A374332_gen(): # generator of terms
a = Fraction(0, 1)
for n in count(1):
yield a.numerator
a = (2*a+Fraction(1, n)) % 1
(PARI) x(n) = if (n==0, 0, 2*x(n-1) + 1/n);
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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