cp's OEIS Frontend

A224927 Denominator of lexicographically least fraction f satisfying floor(f*10^A055642(n)) = n.

%I A224927 #8 Apr 17 2016 04:41:37
%S A224927 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,
%T A224927 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,
%U A224927 11,9,16,7,12,22,5,13,8,11,14,20,3,28,16,13,10,7,11,15
%N A224927 Denominator of lexicographically least fraction f satisfying floor(f*10^A055642(n)) = n.
%C A224927 1 < a(n) <= 10^A055642(n).
%C A224927 For any reduced fraction u/v in the interval [1/10..1[, a(floor(u/v*10^k))=v for k sufficiently large.
%H A224927 Paul Tek, <a href="/A224927/b224927.txt">Table of n, a(n) for n = 1..11000</a>
%e A224927 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...
%e A224927 Hence, a(42)=denominator(3/7)=7.
%o A224927 (PARI) a224927(n) =\
%o A224927 local(a=0, b=1, c, d, e=1, f=0, x=1); \
%o A224927 while(x<=n, x=x*10); \
%o A224927 while(1, c=a+e; d=b+f; \
%o A224927 if(c/d < n/x, a=c; b=d, \
%o A224927 if(c/d >= (n+1)/x, e=c; f=d, \
%o A224927 return(d))))
%Y A224927 Cf. A224926 (numerators), A055642, A002487.
%K A224927 nonn,base,frac
%O A224927 1,1
%A A224927 _Paul Tek_, Apr 20 2013