VOOZH about

URL: https://oeis.org/A224927

⇱ A224927 - OEIS

login
A224927
Denominator of lexicographically least fraction f satisfying floor(f*10^A055642(n)) = n.
2
6, 4, 3, 5, 2, 3, 4, 5, 10, 10, 9, 8, 15, 7, 13, 6, 17, 11, 21, 5, 14, 9, 13, 25, 4, 15, 11, 7, 17, 10, 16, 25, 3, 23, 14, 11, 8, 13, 23, 5, 12, 7, 16, 9, 11, 13, 17, 25, 51, 2, 27, 17, 13, 11, 9, 16, 7, 12, 22, 5, 13, 8, 11, 14, 20, 3, 28, 16, 13, 10, 7, 11, 15
OFFSET
1,1
COMMENTS
1 < a(n) <= 10^A055642(n).
For any reduced fraction u/v in the interval [1/10..1[, a(floor(u/v*10^k))=v for k sufficiently large.
EXAMPLE
The fractions f satisfying floor(f*100)=42, are, in lexicographical order: 3/7, 6/14, 8/19, 9/21, 11/26, 12/28, 14/33, 15/35, 16/38, 17/40, 18/42, 19/45, 20/47, 21/49...
Hence, a(42)=denominator(3/7)=7.
PROG
(PARI) a224927(n) =\
local(a=0, b=1, c, d, e=1, f=0, x=1); \
while(x<=n, x=x*10); \
while(1, c=a+e; d=b+f; \
if(c/d < n/x, a=c; b=d, \
if(c/d >= (n+1)/x, e=c; f=d, \
return(d))))
CROSSREFS
Cf. A224926 (numerators), A055642, A002487.
Sequence in context: A199429 A235509 A346696 * A200104 A154747 A217515
KEYWORD
nonn,base,frac
AUTHOR
Paul Tek, Apr 20 2013
STATUS
approved