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

1,2

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.

Links

Table of n, a(n) for n=1..24.

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

Crossrefs

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

Sequence in context: A004860 A302499 A024662 * A229184 A331203 A302173

Adjacent sequences: A153667 A153668 A153669 * A153671 A153672 A153673

Keyword

nonn,more

Author

Hieronymus Fischer, Jan 06 2009

Extensions

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

Status

approved