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 1-10 of 11 results. Next

A153684 Greatest number m such that the fractional part of (1024/1000)^A153680(n) >= 1-(1/m).

Original entry on oeis.org

1, 93, 123, 1061, 395, 1360, 4137, 2706, 66910, 21740, 15986, 58999, 571666, 1192010, 793642, 1093343, 3476524
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(2)=93, since 1-(1/94)=0.98936...>fract((1024/1000)^A153680(2))=fract((1024/1000)^29)=0.98929...>=1-(1/93).

Crossrefs

Cf. A153664, A153672, A153680, A154130, A153692, A153700, A153708, A153716, A153724.

Formula

a(n):=floor(1/(1-fract((1024/1000)^A153680(n)))), where fract(x) = x-floor(x).

Extensions

a(16) - a(17) from Hagen von Eitzen, May 16 2009

A153672 Numbers k such that the fractional part of (101/100)^k is greater than 1-(1/k).

Original entry on oeis.org

1, 69, 180, 783, 859, 1803, 10763, 19105, 39568, 50172, 132572, 355146, 1452050, 2245950, 3047334, 3933030, 4165171, 98544173
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Comments

Numbers k such that fract((101/100)^k) > 1-(1/k), where fract(x) = x-floor(x).
The next term is greater than 2*10^8.

Examples

			a(2) = 69, since fract((101/100)^69) = 0.9868... > 0.9855... = 1 - (1/69), but fract((101/100)^k) <= 1 - (1/k) for 1 < k < 69.

Crossrefs

Cf. A153664, A154130, A153676, A153680, A153688, A153696, A153704, A153712, A153720.

Programs

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

Extensions

a(13)-a(18) from Robert Gerbicz, Nov 22 2010

A153696 Numbers k such that the fractional part of (10/9)^k is greater than 1-(1/k).

Original entry on oeis.org

1, 6, 13, 17, 5513, 12746, 126237, 430116, 477190, 1295623, 1319307, 3596185, 6109350
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Comments

Numbers k such that fract((10/9)^k) > 1-(1/k), where fract(x) = x-floor(x).
The next such number must be greater than 2*10^5.
a(14) > 10^7. - Robert Price, Mar 24 2019

Examples

			a(3) = 13, since fract((10/9)^13) = 0.9341... > 0.923... = 1 - (1/13), but fract((10/9)^k) <= 1 - (1/k) for 1 < k < 13.

Crossrefs

Cf. A153664, A153672, A153680, A153688, A153700, A154130, A153704, A153712, A153720.

Programs

  • Mathematica
    Select[Range[1000], FractionalPart[(10/9)^#] >= 1 - (1/#) &] (* G. C. Greubel, Aug 24 2016 *)

Extensions

a(8)-a(13) from Hans Havermann, Apr 04 2016

A153704 Numbers k such that the fractional part of e^k is greater than 1-(1/k).

Original entry on oeis.org

1, 8, 19, 178, 209, 1907, 32653, 119136, 220010
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Comments

Numbers k such that fract(e^k) > 1-(1/k), where fract(x) = x-floor(x).
The next such number must be greater than 100000.
a(10) > 300,000. Robert Price, Mar 23 2019

Examples

			a(2)=8, since fract(e^8) = 0.957987... >0.875 = 1-(1/8), but fract(e^k) = 0.389..., 0.085..., 0.598..., 0.413..., 0.428..., 0.633... for 2<=k<=7 which all are less than 1-(1/k).

Crossrefs

Cf. A153664, A153672, A153680, A153688, A153696, A153708, A154130, A153712, A153720.
Cf. A000149.

Programs

  • Mathematica
    Select[Range[2000], N[FractionalPart[E^#], 1000] >= 1 - (1/#) &] (* G. C. Greubel, Aug 25 2016 *)

Extensions

a(8)-a(9) from Robert Price, Mar 23 2019

A153712 Numbers k such that the fractional part of Pi^k is greater than 1-(1/k).

Original entry on oeis.org

1, 2, 15, 22, 58, 109, 157, 1030, 1071, 1274, 2008, 2322, 5269, 151710
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Comments

Numbers k such that fract(Pi^k) > 1-(1/k), where fract(x) = x-floor(x).
The next such number must be greater than 100000.
a(15) > 300000. - Robert Price, Mar 25 2019

Examples

			a(3) = 15, since fract(Pi^15) = 0.969... > 0.933... = 1 - (1/15), but fract(Pi^k) <= 1 - (1/k) for 3 <= k <= 14.

Crossrefs

Cf. A153664, A153672, A153680, A153688, A153696, A153704, A153716, A154130, A153720.
Cf. A001672.

Programs

  • Mathematica
    Select[Range[1000], N[FractionalPart[Pi^#], 100] > 1 - (1/#) &]  (* G. C. Greubel, Aug 25 2016 *)

Extensions

a(14) from Robert Price, Mar 25 2019

A153708 Greatest number m such that the fractional part of e^A153704(n) >= 1-(1/m).

Original entry on oeis.org

3, 23, 27, 261, 348, 2720, 72944, 347065, 244543
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(2) = 23, since 1-(1/24) = 0.9583... > fract(e^A153704(2)) = fract(e^8) = 0.95798... >= 0.95652... >= 1-(1/23).

Crossrefs

Cf. A153664, A153672, A153680, A153688, A153696, A153704, A154130, A153716, A153724.
Cf. A000149.

Programs

  • Mathematica
    A153704 = {1, 8, 19, 178, 209, 1907, 32653, 119136, 220010};
Table[fp = FractionalPart[E^A153704[[n]]]; m = Floor[1/fp];
While[fp >= 1 - (1/m), m++]; m - 1, {n, 1, Length[A153704]}] (* Robert Price, May 10 2019 *)

Formula

a(n) = floor(1/(1-fract(e^A153704(n)))), where fract(x) = x-floor(x).

Extensions

a(8)-a(9) from Robert Price, May 10 2019

A153716 Greatest number m such that the fractional part of Pi^A153712(n) >= 1-(1/m).

Original entry on oeis.org

1, 7, 32, 53, 189, 131, 2665, 10810, 2693, 1976, 3697, 4289, 26577, 483367
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(3) = 32, since 1-(1/33) = 0.9696... > fract(Pi^A153712(3)) = fract(Pi^15) = 0.96938... >= 0.96875 = 1-(1/32).

Crossrefs

Cf. A153664, A153672, A153680, A153688, A153696, A153704, A153712, A154130, A153724.
Cf. A001672.

Programs

  • Mathematica
    A153712 = {1, 2, 15, 22, 58, 109, 157, 1030, 1071, 1274, 2008, 2322,
   5269, 151710};
Table[Floor[1/(1 - FractionalPart[Pi^A153712[[n]]])], {n, 1,
Length[A153712]}] (* Robert Price, May 10 2019 *)

Formula

a(n) = floor(1/(1-fract(Pi^A153712(n)))), where fract(x) = x-floor(x).

Extensions

a(14) from Robert Price, May 10 2019

A153720 Numbers k such that the fractional part of (Pi-2)^k is greater than 1-(1/k).

Original entry on oeis.org

1, 5, 8, 85, 911, 2921, 4491, 11543, 15724, 27683, 29921, 37276, 126659
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Comments

Numbers k such that fract((Pi-2)^k) > 1-(1/k), where fract(x) = x-floor(x).
The next such number must be greater than 200000.
a(14) > 300000. - Robert Price, Mar 26 2019

Examples

			a(3) = 8, since fract((Pi-2)^8) = 0.8846247315... > 0.875 = 1 - (1/8), but fract((Pi-2)^k) = 0.2134..., 0.5268... <= 1 - (1/k) for 6 <= k <= 7.

Crossrefs

Cf. A153664, A153672, A153680, A153688, A153696, A153704, A153712, A153724, A154130.

Programs

  • Mathematica
    Select[Range[1000], N[FractionalPart[(Pi - 2)^#], 100] > 1 - (1/#) &] (* G. C. Greubel, Aug 25 2016 *)

A153724 Greatest number m such that the fractional part of (Pi-2)^A153720(n) >= 1-(1/m).

Original entry on oeis.org

1, 16, 8, 158, 946, 8786, 16159, 20188, 61392, 34039, 31425, 59154, 217556
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(4)=158, since 1-(1/159) = 0.993710... > fract((Pi-2)^A153720(4)) = fract(Pi^85) = 0.993693... >= 0.993670... = 1-(1/158).

Crossrefs

Cf. A153664, A153672, A153680, A153688, A153696, A153704, A153712, A153720, A154130.

Programs

  • Mathematica
    A153720 = {1, 5, 8, 85, 911, 2921, 4491, 11543, 15724, 27683, 29921,
   37276, 126659};
Table[Floor[1/(1 - FractionalPart[(Pi - 2)^A153720[[n]]])], {n, 1,
Length[A153720]}] (* Robert Price, May 10 2019 *)

Formula

a(n):=floor(1/(1-fract((Pi-2)^A153720(n)))), where fract(x) = x-floor(x).

A153700 Greatest number m such that the fractional part of (10/9)^A153696(n) >= 1-(1/m).

Original entry on oeis.org

1, 8, 15, 264, 8741, 15912, 409895
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(3)=15, since 1-(1/16)=0.9375>fract((10/9)^A153696(3))=fract((10/9)^13)=0.9341...>=1-(1/15).

Crossrefs

Cf. A153664, A153672, A153680, A153688, A153696, A154130, A153708, A153716, A153724.

Formula

a(n):=floor(1/(1-fract((10/9)^A153696(n)))), where fract(x) = x-floor(x).
Showing 1-10 of 11 results. Next

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