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A153670
Numbers k such that the fractional part of (101/100)^k is less than 1/k.
14
1, 2, 3, 4, 5, 6, 7, 8, 9, 70, 209, 241, 378, 2697, 4806, 173389, 529938, 1334508, 1572706, 7840546, 15896994, 20204295, 71074288, 119325567
OFFSET
1,2
COMMENTS
Numbers k such that fract((101/100)^k) < 1/k, where fract(x) = x-floor(x).
The next term is greater than 2*10^8.
EXAMPLE
a(10) = 70 since fract((101/100)^70) = 0.006... < 1/10, but fract((101/100)^k) > 0.1 >= 1/k for 10 <= k <= 69.
MATHEMATICA
Select[Range[1000], FractionalPart[(101/100)^#] < (1/#) &] (* G. C. Greubel, Aug 24 2016 *)
PROG
(Python)
from itertools import count, islice
def A153670gen(): # generator of terms
k10, k11 = 100, 101
for k in count(1):
if (k11 % k10)*k < k10:
yield k
k10 *= 100
k11 *= 101
A153670_list = list(islice(A153670gen(), 16)) # Chai Wah Wu, Dec 23 2021
KEYWORD
nonn,more
AUTHOR
Hieronymus Fischer, Jan 06 2009
EXTENSIONS
a(18)-a(24) from Robert Gerbicz, Nov 29 2010
STATUS
approved