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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A153666 Greatest number m such that the fractional part of (3/2)^A153662(n) <= 1/m.

Original entry on oeis.org

2, 4, 16, 11, 16799, 11199, 5536, 92694, 61796, 41197, 23242, 55710, 137921, 257825, 5271294, 706641581, 471094387, 314062925
Offset: 1

Views

Author

Hieronymus Fischer, Dec 31 2008

Keywords

Examples

			a(3)=16 since 1/17<fract((3/2)^A153662(3))=fract((3/2)^4)=0.0625=1/16.

Crossrefs

Cf. A002379, A081464, A153662, A153663, A153664, A153665, A153667, A153668.

Programs

  • Mathematica
    A153662 = {1, 2, 4, 7, 3328, 3329, 4097, 12429, 12430, 12431, 18587, 44257, 112896, 129638, 4264691, 144941960, 144941961, 144941962};
Table[fp = FractionalPart[(3/2)^A153662[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++];  m - 1, {n, 1, Length[A153662]}] (* Robert Price, Mar 26 2019 *)

Formula

a(n):=floor(1/fract((3/2)^A153662(n))), where fract(x) = x-floor(x).

Extensions

a(15)-a(18) from Robert Price, May 09 2012

A153667 Greatest number m such that the fractional part of (3/2)^A153663(n) >= 1-(1/m).

Original entry on oeis.org

2, 2, 2, 2, 3, 14, 31, 33, 69, 137, 222, 318, 901, 1772, 2747, 12347, 16540, 18198, 135794, 222246, 570361, 2134829, 6901329, 75503109, 814558605
Offset: 1

Views

Author

Hieronymus Fischer, Dec 31 2008

Keywords

Examples

			a(5)=3, since 1-(1/4)=0.75>fract((3/2)^A153663(5))=fract((3/2)^12)=0.746...>=1-(1/3).

Crossrefs

Cf. A002379, A081464, A153662, A153663, A153664, A153665, A153666, A153668.

Programs

  • Mathematica
    A153663 = {1, 5, 8, 10, 12, 14, 46, 58, 105, 157, 163, 455, 1060, 1256, 2677, 8093, 28277, 33327, 49304, 158643, 164000, 835999, 2242294, 25380333, 92600006};
Table[fp = FractionalPart[(3/2)^A153663[[n]]]; m = Floor[1/(1-fp)];
While[fp >= 1 - (1/m), m++]; m - 1, {n, 1, Length[A153663]}] (* Robert Price, Mar 26 2019 *)

Formula

a(n) = floor(1/(1-fract((3/2)^A153663(n)))), where fract(x) = x-floor(x).

Extensions

a(22)-a(25) from Robert Price, May 10 2012

A153668 Greatest number m such that the fractional part of (3/2)^A153664(n) >= 1-(1/m).

Original entry on oeis.org

2, 14, 222, 1772, 2747, 12347, 135794, 90529, 222246, 570361, 2134829, 6901329, 4600886, 3067257, 5380892, 75503109, 814558605, 543039070, 362026046, 241350697, 160900465, 107266976, 101721580, 190708740, 127139160
Offset: 1

Views

Author

Hieronymus Fischer, Dec 31 2008

Keywords

Examples

			a(2)=14, since 1-(1/15)=0.933...>fract((3/2)^A153664(2))=fract((3/2)^14)=0.929...>=1-(1/14).

Crossrefs

Cf. A002379, A081464, A153662, A153663, A153664, A153665, A153666, A153667.

Programs

  • Mathematica
    A153664 = {1, 14, 163, 1256, 2677, 8093, 49304, 49305, 158643, 164000, 835999, 2242294, 2242295, 2242296, 3965133, 25380333, 92600006, 92600007, 92600008, 92600009, 92600010, 92600011, 9267816, 125040717, 125040718};
Table[fp = FractionalPart[(3/2)^A153664[[n]]]; m = Floor[1/(1 - fp)];
While[fp >= 1 - (1/m), m++]; m - 1, {n, 1, Length[A153664]}] (* Robert Price, Mar 26 2019 *)

Formula

a(n) = floor(1/(1-fract((3/2)^A153664(n)))), where fract(x) = x-floor(x).

Extensions

a(11)-a(25) from Robert Price, May 10 2012

A153717 Minimal exponents m such that the fractional part of (Pi-2)^m obtains a minimum (when starting with m=1).

Original entry on oeis.org

1, 20, 23, 24, 523, 2811, 3465, 3776, 4567, 6145, 8507, 9353, 19790, 41136, 62097, 72506, 107346
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Comments

Recursive definition: a(1)=1, a(n) = least number m>a(n-1) such that the fractional part of (Pi-2)^m is less than the fractional part of (Pi-2)^k for all k, 1<=k
The next such number must be greater than 200000.
a(18) > 300000. - Robert Price, Mar 26 2019

Examples

			a(3)=23, since fract((Pi-2)^23)=0.0260069.., but fract((Pi-2)^k)>=0.1326... for 1<=k<=22; thus fract((Pi-2)^23)<fract((Pi-2)^k) for 1<=k<23.

Crossrefs

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

Programs

  • Mathematica
    $MaxExtraPrecision = 100000;
p = 1; Select[Range[1, 10000],
 If[FractionalPart[(Pi - 2)^#] < p, p = FractionalPart[(Pi - 2)^#];
True] &] (* Robert Price, Mar 26 2019 *)

Formula

Recursion: a(1):=1, a(k):=min{ m>1 | fract((Pi-2)^m) < fract((Pi-2)^a(k-1))}, where fract(x) = x-floor(x).

A153705 Greatest number m such that the fractional part of e^A153701(n) <= 1/m.

Original entry on oeis.org

1, 2, 11, 11, 23, 28, 69, 85, 115, 964, 1153, 1292, 1296, 1877, 34015, 156075, 952945
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(3)=11 since 1/12 < fract(e^A153701(3)) = fract(e^3) = 0.0855... <= 1/11.

Crossrefs

Cf. A081464, A153669, A153677, A153685, A153693, A153701, A154130, A153713, A153721.
Cf. A000149.

Programs

  • Mathematica
    A153701 = {1, 2, 3, 9, 29, 45, 75, 135, 219, 732, 1351, 3315, 4795,
   4920, 5469, 28414, 37373};
Table[fp = FractionalPart[E^A153701[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A153701]}] (* Robert Price, Mar 25 2019 *)

Formula

a(n) = floor(1/fract(e^A153701(n))), where fract(x) = x-floor(x).

A153721 Greatest number m such that the fractional part of (Pi-2)^A153717(n) <= 1/m.

Original entry on oeis.org

7, 7, 38, 318, 393, 396, 484, 2076, 2619, 4099, 5264, 8556, 18070, 20732, 27209, 73351, 356362
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(3)=38 since 1/39<fract((Pi-2)^A153717(3))=fract((Pi-2)^23)=0.02600...<=1/38.

Crossrefs

Cf. A081464, A153669, A153677, A153685, A153693, A153701, A137994, A153717, A154130.

Programs

  • Mathematica
    A153717 = {1, 20, 23, 24, 523, 2811, 3465, 3776, 4567, 6145, 8507, 9353, 19790, 41136, 62097, 72506, 107346};
Table[fp = FractionalPart[(Pi - 2)^A153717[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A153717]}] (* Robert Price, Mar 26 2019 *)

Formula

a(n) = floor(1/fract((Pi-2)^A153717(n))), where fract(x) = x-floor(x).

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

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

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

A153681 Greatest number m such that the fractional part of (1024/1000)^A153677(n) <= 1/m.

Original entry on oeis.org

41, 60, 76, 116, 233, 463, 718, 1350, 12472, 13733, 17428, 27955, 32276, 41155, 62437, 69643, 111085, 811799, 2656810, 11462221, 56414953
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(2)=60 since 1/61 < fract((1024/1000)^A153677(2)) = fract((1024/1000)^68) = 0.0164... <= 1/60.

Crossrefs

Cf. A081464, A153669, A153677, A154130, A153689, A153697, A153705, A153713, A153721.

Programs

  • Mathematica
    A153677 = {1, 68, 142, 341, 395, 490, 585, 1164, 1707, 26366, 41358,
   46074, 120805, 147332, 184259, 205661, 385710, 522271, 3418770,
   3675376, 9424094};
Table[fp = FractionalPart[(1024/1000)^A153677[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A153677]}] (* Robert Price, Mar 25 2019 *)

Formula

a(n) = floor(1/fract((1024/1000)^A153677(n))), where fract(x) = x-floor(x).

Extensions

a(18)-a(21) from Robert Price, Mar 25 2019
Previous Showing 11-20 of 22 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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