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 1-5 of 5 results.

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

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

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 1-5 of 5 results.

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