The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A265272 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A265272

Least real z > 1/3 such that 1/2 = Sum_{n>=1} {n*z} / 2^n, where {x} denotes the fractional part of x.
(history; published version)

#17 by Charles R Greathouse IV at Tue May 14 21:21:17 EDT 2019

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#16 by Charles R Greathouse IV at Tue May 14 21:21:09 EDT 2019

LINKS

<a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

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#15 by Paul D. Hanna at Tue Dec 15 12:54:05 EST 2015

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#14 by Paul D. Hanna at Tue Dec 15 12:54:03 EST 2015

KEYWORD

nonn,cons,new

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#13 by Paul D. Hanna at Sat Dec 12 12:07:59 EST 2015

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#12 by Paul D. Hanna at Sat Dec 12 12:07:56 EST 2015

EXAMPLE

(the next partial quotient has millions of too many digits to show).

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#11 by Paul D. Hanna at Sat Dec 12 12:07:00 EST 2015

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#10 by Paul D. Hanna at Sat Dec 12 12:06:57 EST 2015

COMMENTS

The rational approximation z ~ 33616604796619977479086259520427152017/85070591730234615865843651857942052860 is accurate to millions many thousands of digits.

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#9 by Paul D. Hanna at Sat Dec 12 11:56:44 EST 2015

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#8 by Paul D. Hanna at Sat Dec 12 11:56:40 EST 2015

COMMENTS

This constant is one of 6 solutions to the equation 1/2 = Sum_{n>=1} {n*z}/2^n, where z is in the interval (0,1) - see cross-references for other solutions.

The complement to this constant is given by A265275.

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approved

editing