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 1-6 of 6 results.

A153702 Numbers k such that the fractional part of e^k is less than 1/k.

Original entry on oeis.org

1, 2, 3, 9, 732, 5469, 28414, 37373, 93638, 136986, 192897
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Comments

Numbers k such that fract(e^k) < 1/k, where fract(x) = x-floor(x).
The next such number must be greater than 100000.
a(12) > 300000. - Robert Price, Mar 23 2019

Examples

			a(4) = 9 since fract(e^9) = 0.08392... < 1/9, but fract(e^k) = 0.598..., 0.413..., 0.428..., 0.633..., 0.957... for 4 <= k <= 8, which are all greater than 1/k.
		

Crossrefs

Programs

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

Extensions

a(10)-a(11) from Robert Price, Mar 23 2019

A153698 Greatest number m such that the fractional part of (10/9)^A153694(n) <= 1/m.

Original entry on oeis.org

9, 4, 11, 82, 6131, 4549, 26735, 8620, 14923, 20328, 151439, 227416, 771341, 2712159, 2676962, 2409266, 4490404, 4041364
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(3) = 11 since 1/12 < fract((10/9)^A153694(3)) = fract((10/9)^7) = 0.09075... <= 1/11.
		

Crossrefs

Formula

a(n) = floor(1/fract((10/9)^A153694(n))), where fract(x) = x - floor(x).

Extensions

a(14)-a(18) from Jinyuan Wang, Mar 03 2020

A153682 Greatest number m such that the fractional part of (1024/1000)^A153678(n) <= 1/m.

Original entry on oeis.org

41, 20, 13, 10, 7, 6, 718, 1350, 12472, 811799, 11462221, 8698270, 56414953
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(5) = 7 since 1/8 < fract((1024/1000)^A153678(5)) = fract((1024/1000)^5) = 0.12589... <= 1/7.
		

Crossrefs

Formula

a(n) = floor(1/fract((1024/1000)^A153678(n))), where fract(x) = x - floor(x).

Extensions

a(10)-a(13) from Jinyuan Wang, Mar 03 2020

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

A153690 Greatest number m such that the fractional part of (11/10)^A153686(n) <= 1/m.

Original entry on oeis.org

10, 4, 3, 18, 253, 58, 618, 484, 6009, 6767, 21386, 697723, 634293, 189959, 4186162, 31102351
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(4) = 18 since 1/19 < fract((11/10)^A153686(4)) = fract((11/10)^17) = 0.05447... <= 1/18.
		

Crossrefs

Formula

a(n) = floor(1/fract((11/10)^A153686(n))), where fract(x) = x - floor(x).

Extensions

a(14)-a(16) from Jinyuan Wang, Mar 03 2020

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

Views

Author

Hieronymus Fischer, Jan 11 2009

Keywords

Examples

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

Crossrefs

Formula

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

Extensions

a(10)-a(15) from Jinyuan Wang, Mar 03 2020
Showing 1-6 of 6 results.