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

A127029 Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that f(n) - floor(f(n)) < 1/10^4.

Original entry on oeis.org

652, 2608, 5868, 14370, 22905, 23325, 28201, 34218, 45374, 54295, 55003, 59266, 66499, 76750, 87228, 91311, 95041, 160874, 169259, 184867, 192157, 196681, 197869, 206495, 206656, 210532, 210676, 230491, 251572, 273117, 289732, 301417, 311669, 317780, 321484
Offset: 1

Views

Author

Artur Jasinski, Jan 03 2007

Keywords

Crossrefs

Cf. A035484, A127022, A127023, A127024, A127025, A127026, A127027, A127028, A127030.

Programs

  • Mathematica
    $MaxExtraPrecision = 1000; a = {}; Do[If[((Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) > 0) && ((Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) < 10^(-4)), AppendTo[a, x]], {x, 1, 20000}]; a

Extensions

a(5)-a(35) from Jon E. Schoenfield, Sep 04 2017

A035484 Numbers n such that fractional part of e^(Pi*sqrt(n)) > 0.99.

Original entry on oeis.org

6, 17, 18, 22, 25, 37, 43, 58, 59, 67, 74, 149, 163, 177, 232, 267, 326, 386, 522, 566, 638, 719, 790, 792, 928, 986, 1014, 1169, 1245, 1257, 1293, 1326, 1467, 1556, 1850, 1872, 1960, 2061, 2086, 2160, 2196, 2208, 2278, 2403, 2438, 2551, 2653, 2795, 2829
Offset: 1

Views

Author

Erich Friedman

Keywords

Comments

Equivalently, let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that ceiling(f(n)) - f(n) < 1/10^2. - Artur Jasinski, Jan 03 2007

Examples

			e^(Pi*sqrt(163)) = 262537412640768743.9999999999992

Links

Crossrefs

Cf. A019296, A127022, A127023, A127024, A127025.

Programs

  • Mathematica
    a = {}; Do[If[(1 - (Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) > 0) && (1 - ( Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]])< 10^(-2)), AppendTo[a, x]], {x, 1, 1000}]; a (* Artur Jasinski, Jan 03 2007 *)
Block[{$MaxExtraPrecision = 1000}, Select[Range@ 3000, And[1 - (#1 - #2) > 0, 1 - (#1 - #2) < 10^(-2)] & @@ {#, Floor@ #} &@ Exp[Pi*Sqrt[#]] &]] (* Michael De Vlieger, Sep 04 2017 *)

Extensions

Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar

A127022 Let f(k) = exp(Pi*sqrt(k)); sequence gives numbers k such that ceiling(f(k)) - f(k) < 1/10^3.

Original entry on oeis.org

25, 37, 43, 58, 67, 74, 163, 232, 522, 719, 1169, 1245, 1467, 1850, 1872, 2086, 3368, 4075, 5773, 7685, 7802, 7942, 8325, 9728, 10032, 11682, 12158, 13574, 17908, 18505, 19183, 19396, 20039, 20244, 20584, 22241, 23773, 23778, 23834, 25004, 27573, 28071, 32497
Offset: 1

Views

Author

Artur Jasinski, Jan 03 2007

Keywords

Links

Crossrefs

Cf. A035484, A127023, A127024, A127025.

Programs

  • Magma
    SetDefaultRealField(RealField(500)); R:= RealField(); [n: n in [1..50000] | Ceiling(Exp(Pi(R)*Sqrt(n))) - Exp(Pi(R)*Sqrt(n)) lt 1/1000]; // G. C. Greubel, Jun 02 2019
  • Mathematica
    a = {}; Do[If[(1 - (Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) > 0) && (1 - ( Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]])< 10^(-3)), AppendTo[a, x]], {x, 1, 1000}]; a
Reap[Block[{$MaxExtraPrecision = Infinity}, Do[If[N[FractionalPart[Exp[Pi Sqrt[n]]], 8] > .999, Sow[n]], {n, 2000}]]][[-1, 1]] (* JungHwan Min, Mar 20 2016 *)
  • PARI
    default(realprecision, 500); c(n) = exp(Pi*sqrt(n));
for(n=1, 50000, if( ceil(c(n)) - c(n) <1/1000, print1(n", "))) \\ G. C. Greubel, Jun 02 2019

Extensions

a(16)-a(43) added (from JungHwan Min's b-file) by Jon E. Schoenfield, Sep 04 2017

A127024 Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that ceiling(f(n)) - f(n) < 1/10^5.

Original entry on oeis.org

58, 67, 163, 232, 1467, 4075, 343732, 357711, 478233, 486396, 881967, 1003957, 1033466, 1045512, 1053883, 1091706, 1208198, 1240173, 1341615, 1844122, 1878006, 1964724, 2177184, 2259143, 2276046, 2279335, 2488542, 2691364, 2850458, 3157407, 3262163, 3310971
Offset: 1

Views

Author

Artur Jasinski, Jan 03 2007

Keywords

References

  • J.-P. Serre, "Lectures on the Mordell-Weil theorem".

Links

Crossrefs

Cf. A035484, A127022, A127023, A127025.

Programs

  • Mathematica
    a = {}; Do[If[(1 - (Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) > 0) && (1 - ( Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]])< 10^(-5)), AppendTo[a, x]], {x, 1, 1000}]; a

Extensions

a(6)-a(32) from Jon E. Schoenfield, Sep 04 2017

A127025 Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that ceiling(f(n)) - f(n) < 1/10^6.

Original entry on oeis.org

58, 163, 1467, 478233, 881967, 1053883, 1341615, 1844122, 3498092, 6069493, 6396611, 8707530, 10414308, 13340780, 16039620, 17013933, 17226343, 18577932, 19390220, 21991290, 24529596, 26202225, 26634713, 26651262, 26848308, 27497372, 32149837, 35437319, 35892748
Offset: 1

Views

Author

Artur Jasinski, Jan 03 2007

Keywords

Links

Crossrefs

Cf. A035484, A127022, A127023, A127024.

Programs

  • Mathematica
    a = {}; Do[If[(1 - (Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) > 0) && (1 - ( Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]])< 10^(-6)), AppendTo[a, x]], {x, 1, 1000}]; a
  • PARI
    is(n)=my(t);default(realprecision, 40);default(realprecision, Pi*sqrt(n)\log(10)+40); t=exp(Pi*sqrt(n));ceil(t)-t<1e-6 \\ Charles R Greathouse IV, Feb 20 2012

Extensions

a(4)-a(20) from Charles R Greathouse IV, Feb 20 2012
a(21)-a(36) from Charles R Greathouse IV, Feb 23 2012

A127031 Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that f(n) - floor(f(n)) < 1/10^6.

Original entry on oeis.org

652, 2608, 880111, 2720885, 4089051, 4619054, 5046630, 5409046, 5433402, 5603556, 5645558, 7278138, 7466589, 10037029, 10730786, 10823358, 11540978, 11860073, 12898258, 14554227, 15107659, 15602035, 15896143, 17070573, 18204473, 19252185, 19425342, 19556500
Offset: 1

Views

Author

Artur Jasinski, Jan 03 2007

Keywords

Comments

a(212)=195246501 is the smallest integer such that the fractional part of e^(Pi*sqrt(n)) begins with exactly 8 zeros. - Anthony Canu, Oct 11 2017

Examples

			5 is not in the sequence since exp(Pi*sqrt(5)) = 1124.186... has fractional part 0.186... which is greater than 1/10^6. But exp(Pi*sqrt(652)) has fractional part 0.0000000001637... which is less than 1/10^6, so 652 is in the sequence. - _Michael B. Porter_, Aug 24 2016

Links

Crossrefs

Cf. A035484, A127022, A127023, A127024, A127025, A127026, A127027, A127028, A127029.

Programs

  • Mathematica
    $MaxExtraPrecision = 1000; a = {}; Do[If[((Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) > 0) && ((Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) < 10^(-6)), AppendTo[a, x]], {x, 1, 100000}]; a
  • PARI
    search(a,b)=my(t,prec=default(realprecision), nprec=round(Pi*sqrt(b)/log(10)+20)); default(realprecision,nprec); for(n=floor(a),b,t=exp(Pi*sqrt(n));if(t-floor(t)<.000001, print(n))); default(realprecision,prec) \\ Charles R Greathouse IV, Jul 28 2009

Extensions

a(3)-a(14) from Charles R Greathouse IV, Jul 28 2009
a(15)-a(18) from Anthony Canu, Aug 24 2016
a(19) from Anthony Canu, Aug 31 2016
a(20)-a(28) from Anthony Canu, Mar 03 2017

A127026 Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that f(n)-floor(f(n)) < 1/10.

Original entry on oeis.org

2, 30, 33, 42, 56, 96, 100, 103, 140, 148, 164, 171, 172, 182, 187, 188, 205, 211, 223, 226, 239, 241, 243, 253, 268, 300, 318, 328, 359, 361, 364, 379, 387, 394, 408, 410, 421, 423, 425, 426, 436, 455, 465, 467, 490, 492, 509, 529, 536, 546, 579, 583, 587
Offset: 1

Views

Author

Artur Jasinski, Jan 03 2007

Keywords

Crossrefs

Cf. A035484, A127022, A127023, A127024, A127025, A127027, A127028, A127029, A127030.

Programs

  • Mathematica
    a = {}; Do[If[((Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) > 0) && (( Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]])< 10^(-1)), AppendTo[a, x]], {x, 1, 1000}]; a

A127027 Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that f(n) - floor(f(n)) < 1/10^2.

Original entry on oeis.org

103, 148, 164, 205, 223, 226, 268, 359, 630, 652, 940, 1005, 1194, 1213, 1332, 1353, 1441, 1481, 1519, 1750, 1823, 1825, 1835, 1930, 1951, 1961, 2309, 2339, 2347, 2357, 2498, 2511, 2527, 2554, 2608, 2683, 3086, 3108, 3157, 3377, 3646, 3653, 3656, 3738, 3762
Offset: 1

Views

Author

Artur Jasinski, Jan 03 2007

Keywords

Crossrefs

Cf. A035484, A127022, A127023, A127024, A127025, A127026, A127028, A127029, A127030.

Programs

  • Mathematica
    a = {}; Do[If[((Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) > 0) && (( Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]])< 10^(-2)), AppendTo[a, x]], {x, 1, 1000}]; a
epsQ[n_]:=Module[{c=Exp[Pi*Sqrt[n]],min=1/10^2},0Harvey P. Dale, Apr 06 2012 *)

Extensions

Corrected by Harvey P. Dale, Apr 06 2012
a(27)-a(45) from Jon E. Schoenfield, Sep 04 2017

A127028 Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that f(n) - floor(f(n)) < 1/10^3.

Original entry on oeis.org

148, 268, 652, 1194, 1332, 1519, 2608, 5650, 5774, 5868, 6632, 7260, 9058, 10153, 10210, 11076, 12314, 13049, 13097, 14370, 15696, 16170, 18736, 19571, 21655, 21814, 22905, 23325, 24496, 27435, 28201, 29239, 31214, 34218, 36166, 36287, 38805, 38990, 42761
Offset: 1

Views

Author

Artur Jasinski, Jan 03 2007

Keywords

Crossrefs

Cf. A035484, A127022, A127023, A127024, A127025, A127026, A127027, A127029, A127030.

Programs

  • Mathematica
    a = {}; Do[If[((Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) > 0) && (( Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]])< 10^(-3)), AppendTo[a, x]], {x, 1, 1000}]; a

Extensions

a(7)-a(39) from Jon E. Schoenfield, Sep 04 2017

A127030 Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that f(n) - floor(f(n)) < 1/10^5.

Original entry on oeis.org

652, 2608, 22905, 54295, 95041, 160874, 184867, 470884, 470884, 613399, 674707, 798611, 880111, 895056, 914998, 1024331, 1027117, 1623312, 1678362, 1699773, 1720078, 1826945, 1830202, 2025665, 2089347, 2092092, 2097388, 2133524, 2375222, 2471017, 2614646
Offset: 1

Views

Author

Artur Jasinski, Jan 03 2007

Keywords

Crossrefs

Cf. A035484, A127022, A127023, A127024, A127025, A127026, A127027, A127028, A127029.

Programs

  • Mathematica
    $MaxExtraPrecision = 1000; a = {}; Do[If[((Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) > 0) && ((Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) < 10^(-5)), AppendTo[a, x]], {x, 1, 100000}]; a

Extensions

a(6)-a(31) from Jon E. Schoenfield, Sep 04 2017
Showing 1-10 of 11 results. Next

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

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