OFFSET
1,2
COMMENTS
Recursive definition: a(1)=1, a(n) = least number m>a(n-1) such that the fractional part of (1024/1000)^m is greater than the fractional part of (1024/1000)^k for all k, 1<=k<m.
The next such number must be greater than 5*10^5.
a(40) > 10^7. Robert Price, Mar 16 2019
FORMULA
Recursion: a(1):=1, a(k):=min{ m>1 | fract((1024/1000)^m) > fract((1024/1000)^a(k-1))}, where fract(x) = x-floor(x).
EXAMPLE
a(30)=82, since fract((1024/1000)^82)= 0.99191990..., but fract((1024/1000)^k)<0.9893 for 1<=k<=81; thus fract((1024/1000)^82)>fract((1024/1000)^k) for 1<=k<82 and 82 is the minimal exponent >29 with this property.
MATHEMATICA
$MaxExtraPrecision = 10000;
p = 0;
Select[Range[1, 50000],
If[FractionalPart[(1024/1000)^#] > p,
p = FractionalPart[(1024/1000)^#]; True] &] (* Robert Price, Mar 16 2019 *)
PROG
(Python)
A153679_list, m, n, k, q = [], 1, 1024, 1000, 0
while m < 10**4:
r = n % k
if r > q:
q = r
A153679_list.append(m)
m += 1
n *= 1024
k *= 1000
q *= 1000 # Chai Wah Wu, May 16 2020
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Hieronymus Fischer, Jan 06 2009
EXTENSIONS
a(37)-a(39) from Robert Price, Mar 16 2019
STATUS
approved