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.

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A153713 Greatest number m such that the fractional part of Pi^A137994(n) <= 1/m.

Original entry on oeis.org

7, 159, 270, 307, 744, 757, 796, 1079, 1226, 7804, 13876, 62099, 70718, 86902, 154755
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(2)=159 since 1/160<fract(Pi^A137994(2))=fract(Pi^3)=0.0062766...<=1/159.

Crossrefs

Cf. A081464, A153669, A153677, A153685, A153693, A153701, A137994, A154130, A153721.
Cf. A001672.

Programs

  • Mathematica
    A137994 = {1, 3, 81, 264, 281, 472, 1147, 2081, 3207, 3592, 10479, 12128, 65875, 114791, 118885};
Table[fp = FractionalPart[Pi^A137994[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A137994]}] (* Robert Price, Mar 26 2019 *)

Formula

a(n) = floor(1/fract(Pi^A137994(n))), where fract(x) = x-floor(x).

Extensions

a(14)-a(15) from Robert Price, Mar 26 2019

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

A153697 Greatest number m such that the fractional part of (10/9)^A153693(n) <= 1/m.

Original entry on oeis.org

9, 11, 30, 82, 6131, 26735, 29430, 76172, 151439, 227416, 771341, 2712159, 4490404
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(2)=11 since 1/12 < fract((10/9)^A153693(2)) = fract((10/9)^7) = 0.09075... <= 1/11.

Crossrefs

Cf. A081464, A153669, A153677, A153685, A153693, A154130, A153705, A153713, A153721.

Programs

  • Mathematica
    A153693 = {1, 7, 50, 62, 324, 3566, 66877, 108201, 123956, 132891,
   182098, 566593, 3501843};
Table[fp = FractionalPart[(10/9)^A153693[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A153693]}] (* Robert Price, Mar 25 2019 *)

Formula

a(n) = floor(1/fract((10/9)^A153693(n))), where fract(x) = x-floor(x).

Extensions

a(12)-a(13) from Robert Price, Mar 25 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

Cf. A153662, A153670, A153678, A153686, A153694, A154130, A153706, A153714, A153722.

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

A153699 Greatest number m such that the fractional part of (10/9)^A153695(m) >= 1-(1/m).

Original entry on oeis.org

1, 1, 1, 2, 3, 8, 15, 264, 334, 465, 683, 713, 758, 8741, 15912, 18920, 38560, 409895
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(7)=15, since 1-(1/16)=0.9375>fract((10/9)^A153695(7))=fract((10/9)^13)=0.9341...>=1-(1/15).

Crossrefs

Cf. A153663, A153671, A153679, A153687, A153695, A154130, A153707, A153715, A153723.

Formula

a(n):=floor(1/(1-fract((10/9)^A153695(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).

A153675 Greatest number m such that the fractional part of (101/100)^A153671(m) >= 1-(1/m).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 7, 9, 11, 13, 19, 30, 76, 81, 238, 913, 1334, 4645, 6812, 17396, 351085, 552184
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(5)=1, since 1-(1/2)=0.5>fract((101/100)^A153671(5))=fract((101/100)^5)=0.0510...>=1-(1/1).

Crossrefs

Cf. A153663, A154130, A153667, A153683, A153691, A153699, A153707, A153715, A153723.

Formula

a(n):=floor(1/(1-fract((101/100)^A153671(n)))), where fract(x) = x-floor(x).

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

Cf. A153662, A153670, A153678, A154130, A153690, A153698, A153706, A153714, A153722.

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

A153683 Greatest number m such that the fractional part of (1024/1000)^A153679(m) >= 1-(1/m).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 5, 6, 9, 17, 93, 123, 1061, 1360, 4137, 66910, 571666, 1192010
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(5)=1, since 1-(1/2)=0.5>fract((1024/1000)^A153679(5))=fract((1024/1000)^5)=0.0510...>=1-(1/1).

Crossrefs

Cf. A153663, A153671, A153679, A154130, A153691, A153699, A153707, A153715, A153723.

Formula

a(n):=floor(1/(1-fract((1024/1000)^A153679(n)))), where fract(x) = x-floor(x).

A153689 Greatest number m such that the fractional part of (11/10)^A153685(n) <= 1/m.

Original entry on oeis.org

10, 18, 253, 618, 6009, 6767, 21386, 697723, 4186162, 31102351
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(2)=18 since 1/19 < fract((11/10)^A153685(2)) = fract((11/10)^17) = 0.0544... <= 1/18.

Crossrefs

Cf. A081464, A153669, A153677, A153685, A154130, A153697, A153705, A153713, A153721.

Programs

  • Mathematica
    A153685 = {1, 17, 37, 237, 599, 615, 6638, 13885, 1063942, 9479731};
Table[fp = FractionalPart[(11/10)^A153685[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A153685]}] (* Robert Price, Mar 25 2019 *)

Formula

a(n) = floor(1/fract((11/10)^A153685(n))), where fract(x) = x-floor(x).

Extensions

a(9)-a(10) from Robert Price, Mar 25 2019
Previous Showing 41-50 of 58 results. Next

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