OFFSET
1,2
COMMENTS
Recursive definition: a(1)=1, a(n) = least number m>a(n-1) such that the fractional part of (101/100)^m is greater than the fractional part of (101/100)^k for all k, 1<=k<m.
The next such number must be greater than 10^6.
a(84) > 10^7. Robert Price, Mar 21 2019
FORMULA
Recursion: a(1):=1, a(k):=min{ m>1 | fract((101/100)^m) > fract((101/100)^a(k-1))}, where fract(x) = x-floor(x).
EXAMPLE
a(5)=5, since fract((101/100)^5)=0.05101005, but fract((101/100)^k)=0.01, 0.0201, 0.030301, 0.04060401 for 1<=k<=4; thus fract((101/100)^5)>fract((101/100)^k) for 1<=k<5.
MATHEMATICA
p = 0; Select[Range[1, 20000],
If[FractionalPart[(101/100)^#] > p, p = FractionalPart[(101/100)^#];
True] &] (* Robert Price, Mar 21 2019 *)
PROG
(Python)
A153671_list, m, n, k, q = [], 1, 101, 100, 0
while m < 10**4:
r = n % k
if r > q:
q = r
A153671_list.append(m)
m += 1
n *= 101
k *= 100
q *= 100 # Chai Wah Wu, May 16 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Jan 06 2009
EXTENSIONS
a(72)-a(83) from Robert Price, Mar 21 2019
STATUS
approved