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 1-8 of 8 results.

A153707 Greatest number m such that the fractional part of e^A091560(m) >= 1-(1/m).

Original entry on oeis.org

3, 23, 27, 41, 59, 261, 348, 2720, 3198, 6064, 72944, 347065
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(2)=23, since 1-(1/24) = 0.9583...> fract(e^A091560(2)) = fract(e^8) = 0.95798.. >= 0.95652... >= 1-(1/23).

Crossrefs

Cf. A153663, A153671, A153679, A153687, A153695, A154130, A153715, A153723.
Cf. A000149.

Programs

  • Mathematica
    $MaxExtraPrecision = 100000;
A091560 = {1,8,19,76,166,178,209,1907,20926,22925,32653,119136};
Floor[1/(1-FractionalPart[E^A091560])] (* Robert Price, Apr 18 2019 *)

Formula

a(n):=floor(1/(1-fract(e^A091560(n)))), where fract(x) = x-floor(x).

Extensions

a(12) from Robert Price, Apr 18 2019

A153715 Greatest number m such that the fractional part of Pi^A153711(m) >= 1-(1/m).

Original entry on oeis.org

1, 7, 32, 53, 189, 2665, 10810, 26577, 128778, 483367
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(3) = 32, since 1-(1/33) = 0.9696... > fract(Pi^A153711(3)) = fract(Pi^15) = 0.96938... >= 0.96875 = 1-(1/32).

Crossrefs

Cf. A153663, A153671, A153679, A153687, A153695, A091560, A153711, A154130, A153723.
Cf. A001672.

Programs

  • Mathematica
    $MaxExtraPrecision = 100000;
A153711 = {1, 2, 15, 22, 58, 157, 1030, 5269, 145048, 151710};
Floor[1/(1-FractionalPart[Pi^A153711])] (* Robert Price, Apr 18 2019 *)

Formula

a(n) = floor(1/(1-fract(Pi^A153711(n)))), where fract(x) = x-floor(x).

Extensions

a(9)-a(10) from Robert Price, Apr 18 2019

A153719 Minimal exponents m such that the fractional part of (Pi-2)^m obtains a maximum (when starting with m=1).

Original entry on oeis.org

1, 2, 3, 4, 5, 39, 56, 85, 557, 911, 2919, 2921, 4491, 11543, 15724, 98040, 110932, 126659
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 greater than the fractional part of (Pi-2)^k for all k, 1<=k
The next such number must be greater than 200000.
a(19) > 300000. - Robert Price, Mar 26 2019

Examples

			a(6)=39, since fract((Pi-2)^39)= 0.9586616565..., but fract((Pi-2)^k)<=0.9389018... for 1<=k<=38; thus fract((Pi-2)^39)>fract((Pi-2)^k) for 1<=k<39 and 39 is the minimal exponent > 5 with this property.

Crossrefs

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

Programs

  • Mathematica
    $MaxExtraPrecision = 100000;
p = 0; 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).

A153144 Numbers n such that 2*n+19 is not a prime.

Original entry on oeis.org

1, 3, 4, 7, 8, 10, 13, 15, 16, 18, 19, 22, 23, 25, 28, 29, 31, 33, 34, 36, 37, 38, 40, 43, 46, 48, 49, 50, 51, 52, 53, 55, 57, 58, 61, 62, 63, 64, 67, 68, 70, 71, 73, 75, 76, 78, 79, 82, 83, 84, 85, 88, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101
Offset: 1

Views

Author

Vincenzo Librandi, Dec 19 2008

Keywords

Links

Crossrefs

Cf. A153143, A153081, A155551.
Numbers n such that 2n+k is not prime: A047845 (k=1), A153238 (k=3), A153052 (k=5), A153053 (k=7), A153723 (k=9), A153083 (k=11), A153082 (k=13), A241571 (k=15), A241572 (k=17), this sequence (k=19).

Programs

  • Magma
    [n: n in [1..120] | not IsPrime(2*n + 19)]; // Vincenzo Librandi, Dec 13 2012
  • Mathematica
    Select[Range[0, 500], !PrimeQ[2# + 19] &] (* Vincenzo Librandi, Dec 13 2012 *)

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).

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).

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).

A153691 Greatest number m such that the fractional part of (11/10)^A153687(m) >= 1-(1/m).

Original entry on oeis.org

1, 1, 1, 1, 2, 4, 19, 21, 28, 151, 200, 709, 767, 5727, 15908, 162819, 302991
Offset: 1

Views

Author

Hieronymus Fischer, Jan 06 2009

Keywords

Examples

			a(6)=4, since 1-(1/5)=0.8>fract((11/10)^A153687(6))=fract((11/10)^6)=0.771...>=1-(1/4).

Crossrefs

Cf. A153663, A153671, A153679, A153683, A154130, A153699, A153707, A153715, A153723.

Formula

a(n):=floor(1/(1-fract((11/10)^A153687(n)))), where fract(x) = x-floor(x).
Showing 1-8 of 8 results.

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

Content is available under The OEIS End-User License Agreement.