The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A078607 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A078607

Least positive integer x such that 2*x^n > (x+1)^n.
(history; published version)

#30 by Peter Luschny at Fri May 15 13:00:42 EDT 2020

STATUS

proposed

approved

#29 by Michel Marcus at Fri May 15 01:42:59 EDT 2020

STATUS

editing

proposed

#28 by Michel Marcus at Fri May 15 01:42:55 EDT 2020

FORMULA

a(n) = n/log(2) + O(1). - _Charles R Greathouse IV, _, Oct 31 2013

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proposed

editing

#27 by M. F. Hasler at Thu May 14 11:48:46 EDT 2020

STATUS

editing

proposed

#26 by M. F. Hasler at Thu May 14 11:46:27 EDT 2020

EXAMPLE

a(2) is given by floor(1/(1-1/sqrt(2))). [From former A230748.]

PROG

(PARI) a(n)=1\(1-1/2^(1/n)) \\ Charles R Greathouse IV, Oct 31 2013

STATUS

proposed

editing

Discussion

Thu May 14

11:48

M. F. Hasler: Merged material from duplicate A230748, now killed.

#25 by M. F. Hasler at Thu May 14 11:43:38 EDT 2020

STATUS

editing

proposed

#24 by M. F. Hasler at Thu May 14 11:42:23 EDT 2020

FORMULA

Following formulae merged in from former A230748, M. F. Hasler, May 14 2020:

a(n) = floor(1/(1-1/2^(1/n))).

a(n) = n/log(2) + O(1). - Charles R Greathouse IV, Oct 31 2013

a(n) = floor(1/(1-x)) with x^n = 1/2: f(n) = 1/(2^(1/n)-1) is never an integer for n > 1, whence floor(f(n)+1) = ceiling(f(n)) = a(n). - M. F. Hasler, Nov 02 2013, and Gabriel Conant, May 01 2016

CROSSREFS

Cf. A050499, A050500.

STATUS

approved

editing

#23 by Michel Marcus at Sat May 09 02:45:07 EDT 2020

STATUS

reviewed

approved

#22 by Joerg Arndt at Sat May 09 02:36:58 EDT 2020

STATUS

proposed

reviewed

#21 by M. F. Hasler at Fri May 08 12:47:33 EDT 2020

STATUS

editing

proposed