A153674 -id:A153674 - cp's OEIS frontend

A153670 Numbers k such that the fractional part of (101/100)^k is less than 1/k.

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

Hieronymus Fischer, Jan 06 2009

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.

			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.

Cf. A153662, A154130, A153674, A153678, A153686, A153694, A153702, A153710, A153718.

Select[Range[1000], FractionalPart[(101/100)^#] < (1/#) &] (* G. C. Greubel, Aug 24 2016 *)

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

a(18)-a(24) from Robert Gerbicz, Nov 29 2010

A154135 Greatest number m such that the fractional part of (4/3)^A154131(n) <= 1/m.

Original entry on oeis.org

3, 6, 30, 6430, 4822, 22869, 20551, 224544, 184762, 2396968, 15229280, 3183837, 2387878, 28274047, 7149842

Offset: 1

Hieronymus Fischer, Jan 11 2009

			a(3)=30 since 1/31<fract((4/3)^A154131(3))=fract((4/3)^17)=0.0327357...<=1/30.

Cf. A153666, A153674, A153706, A153714, A154143, A154151.

Cf. A002379, A064628.

a(n) = floor(1/fract((4/3)^A154131(n))), where fract(x) = x - floor(x).

a(10)-a(15) from Jinyuan Wang, Mar 03 2020

cp's OEIS Frontend

A153670 Numbers k such that the fractional part of (101/100)^k is less than 1/k.

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