A161555 Numerators of sequence of fractions of primes that minimize absolute value of difference between the fractions and 1/4.

2, 2, 2, 3, 3, 3, 5, 5, 7, 7, 7, 7, 11, 11, 13, 13, 13, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 37, 37, 37, 41, 41, 43, 43, 43, 43, 43, 43, 43, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 67, 67, 67, 67

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

Crossrefs

Cf. A161554 (denominators).

Sequence in context: A247049 A029059 A035449 * A029058 A046026 A139801

Adjacent sequences: A161552 A161553 A161554 * A161556 A161557 A161558

Keyword

nonn,frac

Author

Daniel Tisdale, Jun 13 2009

Extensions

More terms from Michel Marcus, Jun 12 2013

Status

approved