A161554 Denominators of sequence of fractions of primes that minimize absolute value of difference between the fractions and 1/4.

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

Offset

1,1

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.

Links

Table of n, a(n) for n=1..59.

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,...

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(n)); \\ Michel Marcus, Jun 12 2013 & Mar 21 2016

Crossrefs

Cf. A161555 (numerators).

Sequence in context: A285848 A086527 A361445 * A328944 A353758 A245644

Adjacent sequences: A161551 A161552 A161553 * A161555 A161556 A161557

Keyword

nonn,frac

Author

Daniel Tisdale, Jun 13 2009

Extensions

More terms from Michel Marcus, Jun 12 2013

Status

approved