cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A153678 Numbers k such that the fractional part of (1024/1000)^k is less than 1/k.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 585, 1164, 1707, 522271, 3675376, 3906074, 9424094
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Comments

Numbers k such that fract((1024/1000)^k) < 1/k, where fract(x) = x-floor(x).
The next such number must be greater than 5*10^5.
a(14) > 10^7. - Robert Price, Mar 16 2019

Examples

			a(7) = 585 since fract((1024/1000)^585) = 0.00139... < 1/585, but fract((1024/1000)^k) >= 1/k for 7 <= k <= 584.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[2000], FractionalPart[(1024/1000)^#] < (1/#) &] (* G. C. Greubel, Aug 24 2016; corrected by Robert Price, Mar 16 2019 *)
  • PARI
    isok(n) = frac((1024/1000)^n) < 1/n \\ Michel Marcus, Aug 06 2013

Extensions

a(10)-a(13) from Robert Price, Mar 16 2019

A153686 Numbers k such that the fractional part of (11/10)^k is less than 1/k.

Original entry on oeis.org

1, 2, 3, 17, 37, 48, 237, 420, 599, 615, 6638, 13885, 13886, 62963, 1063942, 9479731
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Comments

Numbers k such that fract((11/10)^k) < 1/k, where fract(x) = x-floor(x).
The next such number must be greater than 2*10^5.
a(17) > 10^7. - Robert Price, Mar 19 2019

Examples

			a(4) = 17 since fract((11/10)^17) = 0.05447... < 1/17, but fract((11/10)^k) >= 1/k for 4 <= k <= 16.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[1000], FractionalPart[(11/10)^#] < (1/#) &] (* G. C. Greubel, Aug 24 2016 *)
  • Python
    A153686_list, k, k10, k11 =  [], 1, 10, 11
    while k < 10**6:
        if (k11 % k10)*k < k10:
            A153686_list.append(k)
        k += 1
        k10 *= 10
        k11 *= 11 # Chai Wah Wu, Apr 01 2021

Extensions

a(15)-a(16) from Robert Price, Mar 19 2019

A153674 Greatest number m such that the fractional part of (101/100)^A153670(n) <= 1/m.

Original entry on oeis.org

100, 49, 33, 24, 19, 16, 13, 12, 10, 147, 703, 676, 932, 3389, 7089, 1129226, 1741049, 1356464, 1960780, 11014240, 75249086, 28657625, 132665447, 499298451
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(5) = 19 since 1/20 < fract((101/100)^A153670(5)) = fract((101/100)^5) = 0.0510... <= 1/19.
		

Crossrefs

Formula

a(n) = floor(1/fract((101/100)^A153670(n))), where fract(x) = x - floor(x).

Extensions

a(18)-a(24) from Jinyuan Wang, Mar 03 2020
Showing 1-3 of 3 results.