A374333 -id:A374333 - cp's OEIS frontend

A374335 a(n) is the denominator of x(n) = (16x(n-1) + (120n^2 - 89n + 16)/(512n^4 - 1024n^3 + 712n^2 - 206*n + 21)) mod 1, with x(0) = 0.

1, 15, 4095, 765765, 111035925, 78058255275, 24536311574775, 81926744348173725, 154923473562396513975, 154923473562396513975, 595232293160786606325, 76784965817741472215925, 321191512015612578279214275, 3146713243216956429401462252175, 342991743510648250804759385487075

Offset: 0

Paolo Xausa, Jul 06 2024

See A374334 for details and links.

Paolo Xausa, Table of n, a(n) for n = 0..375

Cf. A374333, A374334 (numerators), A374581, A374608.

Block[{n = 0}, Denominator[NestList[Mod[16*# + (120*(++n)^2 - 89*n + 16)/(512*n^4 - 1024*n^3 + 712*n^2 - 206*n + 21), 1] &, 0, 20]]]

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

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Jul 06 2024

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).
Denominators are given by A374333.

Paolo Xausa, Table of n, a(n) for n = 0..2000
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).
David H. Bailey and Richard E. Crandall, Random Generators and Normal Numbers, Experimental Mathematics, Vol. 11 (2002), Issue 4, pp. 527-546 (preprint draft).

Cf. A002162, A374333 (denominators), A374334, A374336.

Block[{n = 0}, Numerator[NestList[Mod[2*# + 1/++n, 1] &, 0, 50]]]

x(n) = if (n==0, 0, 2*x(n-1) + 1/n);
a(n) = numerator(frac(x(n))); \\ Michel Marcus, Jul 13 2024

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
A374332_list = list(islice(A374332_gen(),20)) # Chai Wah Wu, Jul 13 2024

cp's OEIS Frontend

A374335 a(n) is the denominator of x(n) = (16x(n-1) + (120n^2 - 89n + 16)/(512n^4 - 1024n^3 + 712n^2 - 206*n + 21)) mod 1, with x(0) = 0.

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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.

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cp's OEIS Frontend

A374335 a(n) is the denominator of x(n) = (16*x(n-1) + (120*n^2 - 89*n + 16)/(512*n^4 - 1024*n^3 + 712*n^2 - 206*n + 21)) mod 1, with x(0) = 0.

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Programs

Mathematica

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

Views

Author

Keywords

Comments

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Crossrefs

Programs

Mathematica

PARI

Python

A374335 a(n) is the denominator of x(n) = (16x(n-1) + (120n^2 - 89n + 16)/(512n^4 - 1024n^3 + 712n^2 - 206*n + 21)) mod 1, with x(0) = 0.