The On-Line Encyclopedia of Integer Sequences (OEIS)

The OEIS is supported by the many generous donors to the OEIS Foundation.

Revision History for A161554

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

Denominators of sequence of fractions of primes that minimize absolute value of difference between the fractions and 1/4.
(history; published version)

#8 by Bruno Berselli at Mon Mar 21 06:21:06 EDT 2016

STATUS

proposed

approved

#7 by Michel Marcus at Mon Mar 21 04:08:24 EDT 2016

STATUS

editing

proposed

#6 by Michel Marcus at Mon Mar 21 04:08:18 EDT 2016

PROG

(PARI) afr(n) = {kdiff = 1; fp = primes(n); for (i=1, n, num = fp[i]; for (j=1, n, den = fp[j]; diff = abs(num/den - 1/4); if (diff <= kdiff, kdiff = diff; knum = num; kden = den; ); ); ); return(knum/kden); }

a(n) = denominator(afr(PARIn)) ; \\ see prog in A161555._Michel Marcus_, Jun 12 2013 & Mar 21 2016

STATUS

approved

editing

#5 by Joerg Arndt at Wed Jun 12 14:06:09 EDT 2013

STATUS

proposed

approved

#4 by Michel Marcus at Wed Jun 12 13:44:32 EDT 2013

STATUS

editing

proposed

#3 by Michel Marcus at Wed Jun 12 13:41:53 EDT 2013

NAME

Denominators of sequence of fractions of primes that minimize absolute value of difference between the fractions and 1/4. For n = 2, there are two primes available for use in numerator or denominator: 2,3. The best approximation to 1/4 is 2/3. Sequence begins at n = 2.

DATA

3, 5, 7, 11, 13, 13, 19, 19, 29, 29, 29, 29, 43, 43, 53, 53, 53, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 149, 149, 149, 163, 163, 173, 173, 173, 173, 173, 173, 173, 211, 211, 211, 211, 211, 211, 211, 211, 211, 211, 269, 269, 269, 269

COMMENTS

For n = 2, there are two primes available for use in numerator or denominator: 2,3. The best approximation to 1/4 is 2/3. Sequence begins at n = 2.

PROG

(PARI) \\ see prog in A161555.

CROSSREFS

Cf. A161555 (numerators).

KEYWORD

nonn,frac

EXTENSIONS

More terms from Michel Marcus, Jun 12 2013

STATUS

approved

editing

#2 by Russ Cox at Sat Mar 31 10:31:25 EDT 2012

AUTHOR

_Daniel Tisdale (daniel6874(AT)gmail.com), _, Jun 13 2009

Discussion

Sat Mar 31

10:31

OEIS Server: https://oeis.org/edit/global/716

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

DATA

3, 5, 7, 11, 13, 13, 19, 19, 29

OFFSET

1,1

EXAMPLE

For n=2, there are two primes available to approximate 1/4. The closest fraction in absolute value is 2/3. The first few approximating fractions are: 2/3, 2/5, 2/7, 3/11, 3/13,...

KEYWORD

nonn

AUTHOR

Daniel Tisdale (daniel6874(AT)gmail.com), Jun 13 2009

STATUS

approved