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 20 results. Next

A217865 First differences of A050504.

Original entry on oeis.org

1, 2, 2, 3, 2, 3, 3, 3, 4, 3, 3, 4, 3, 4, 4, 4, 4, 3, 4, 4, 5, 4, 4, 4, 4, 4, 5, 4, 5, 4, 4, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 6, 5, 5, 5, 6, 5, 5, 6, 5, 5, 6, 5, 5, 6, 5, 6, 5, 6, 5, 6
Offset: 1

Views

Author

Jon Perry, Oct 13 2012

Keywords

Crossrefs

Cf. A050504.

Programs

  • JavaScript
    for (i=1;i<88;i++)
document.write(Math.floor((i+1)*Math.log(i+1))-Math.floor(i*Math.log(i))+", ");

Formula

a(n) = A050504(n+1) - A050504(n).

A212455 a(n) = floor(2n*log(2n)).

Original entry on oeis.org

1, 5, 10, 16, 23, 29, 36, 44, 52, 59, 68, 76, 84, 93, 102, 110, 119, 129, 138, 147, 156, 166, 176, 185, 195, 205, 215, 225, 235, 245, 255, 266, 276, 286, 297, 307, 318, 329, 339, 350, 361, 372, 383, 394, 404, 416, 427
Offset: 1

Views

Author

Mohammad K. Azarian, May 31 2012

Keywords

Links

Crossrefs

Cf. A050502, A050504, A212456, A212457, A212458, A212459, A212460, A212461, A212462.

Programs

  • Derive
    PROG(y := [], x := 100, LOOP(IF(x = 0, RETURN y), y := ADJOIN(FLOOR(2·x·LOG(2·x)), y), x := x - 1))
  • Magma
    [Floor(2*n*Log(2*n)): n in [1..80]]; // Vincenzo Librandi, Feb 13 2013
  • Mathematica
    Table[Floor[2*n*Log[2*n]], {n, 60}] (* Vincenzo Librandi, Feb 13 2013 *)
  • PARI
    a(n)=2*n*log(2*n)\1 \\ Charles R Greathouse IV, Sep 04 2015

A212456 a(n) = floor(3n*log(3n)).

Original entry on oeis.org

3, 10, 19, 29, 40, 52, 63, 76, 88, 102, 115, 129, 142, 156, 171, 185, 200, 215, 230, 245, 261, 276, 292, 307, 323, 339, 355, 372, 388, 404, 421, 438, 454, 471, 488, 505, 522, 539, 557, 574, 591, 609, 626, 644, 662, 679
Offset: 1

Views

Author

Mohammad K. Azarian, May 31 2012

Keywords

Links

Crossrefs

Cf. A050502, A050504, A212455, A212457, A212458, A212459, A212460, A212461, A212462.

Programs

  • Derive
    PROG(y := [], x := 100, LOOP(IF(x = 0, RETURN y), y := ADJOIN(FLOOR(3·x·LOG(3·x)), y), x := x - 1))
  • Magma
    [Floor(3*n*Log(3*n)): n in [1..80]]; // Vincenzo Librandi, Feb 13 2013
  • Mathematica
    Table[Floor[3*n*Log[3*n]], {n, 60}] (* Vincenzo Librandi, Feb 13 2013 *)
  • PARI
    a(n)=3*n*log(3*n)\1 \\ Charles R Greathouse IV, Sep 04 2015

A212457 a(n) = floor(4n*log(4n)).

Original entry on oeis.org

5, 16, 29, 44, 59, 76, 93, 110, 129, 147, 166, 185, 205, 225, 245, 266, 286, 307, 329, 350, 372, 394, 416, 438, 460, 483, 505, 528, 551, 574, 597, 621, 644, 668, 691, 715, 739, 763, 787, 812, 836, 860, 885, 910, 934
Offset: 1

Views

Author

Mohammad K. Azarian, May 31 2012

Keywords

Links

Crossrefs

Cf. A050502, A050504, A212455, A212456, A212458, A212459, A212460, A212461, A212462.

Programs

  • Derive
    PROG(y := [], x := 100, LOOP(IF(x = 0, RETURN y), y := ADJOIN(FLOOR(4·x·LOG(4·x)), y), x := x - 1))
  • Magma
    [Floor(4*n*Log(4*n)): n in [1..80]]; // Vincenzo Librandi, Feb 13 2013
  • Mathematica
    Table[Floor[4*n*Log[4*n]], {n, 80}] (* Vincenzo Librandi, Feb 13 2013 *)
  • PARI
    a(n)=4*n*log(4*n)\1 \\ Charles R Greathouse IV, Sep 04 2015

A212458 a(n) = floor(5n*log(5n)).

Original entry on oeis.org

8, 23, 40, 59, 80, 102, 124, 147, 171, 195, 220, 245, 271, 297, 323, 350, 377, 404, 432, 460, 488, 517, 545, 574, 603, 632, 662, 691, 721, 751, 781, 812, 842, 873, 903, 934, 965, 996, 1028, 1059, 1091, 1122, 1154, 1186
Offset: 1

Views

Author

Mohammad K. Azarian, May 31 2012

Keywords

Links

Crossrefs

Cf. A050502, A050504, A212455, A212456, A212457, A212459, A212460, A212461, A212462.

Programs

  • Derive
    PROG(y := [], x := 100, LOOP(IF(x = 0, RETURN y), y := ADJOIN(FLOOR(5·x·LOG(5·x)), y), x := x - 1))
  • Magma
    [Floor(5*n*Log(5*n)): n in [1..80]]; // Vincenzo Librandi, Feb 13 2013
  • Mathematica
    Table[Floor[5*n*Log[5*n]], {n, 80}] (* Vincenzo Librandi, Feb 13 2013 *)
  • PARI
    a(n)=5*n*log(5*n)\1 \\ Charles R Greathouse IV, Sep 04 2015

A212459 a(n) = ceiling(2n*log(2n)).

Original entry on oeis.org

2, 6, 11, 17, 24, 30, 37, 45, 53, 60, 69, 77, 85, 94, 103, 111, 120, 130, 139, 148, 157, 167, 177, 186, 196, 206, 216, 226, 236, 246, 256, 267, 277, 287, 298, 308, 319, 330, 340, 351, 362, 373, 384, 395, 405, 417, 428
Offset: 1

Views

Author

Mohammad K. Azarian, May 31 2012

Keywords

Links

Crossrefs

Cf. A050502, A050504, A212455, A212456, A212457, A212458, A212460, A212461, A212462.

Programs

  • Derive
    PROG(y := [], x := 100, LOOP(IF(x = 0, RETURN y), y := ADJOIN(CEILING(2·x·LOG(2·x)), y), x := x - 1))
  • Magma
    [Ceiling(2*n*Log(2*n)): n in [1..80]]; // Vincenzo Librandi, Feb 13 2013
  • Mathematica
    Table[Ceiling[2*n*Log[2*n]], {n, 80}] (* Vincenzo Librandi, Feb 13 2013 *)
  • PARI
    a(n) = ceil(2*n*log(2*n)); \\ Michel Marcus, Jan 11 2016

Formula

a(n) = A050502(2*n). - Michel Marcus, Jan 11 2016

A212460 a(n) = ceiling(3n*log(3n)).

Original entry on oeis.org

4, 11, 20, 30, 41, 53, 64, 77, 89, 103, 116, 130, 143, 157, 172, 186, 201, 216, 231, 246, 262, 277, 293, 308, 324, 340, 356, 373, 389, 405, 422, 439, 455, 472, 489, 506, 523, 540, 558, 575, 592, 610, 627, 645, 663, 680
Offset: 1

Views

Author

Mohammad K. Azarian, May 31 2012

Keywords

Links

Crossrefs

Cf. A050502, A050504, A212455, A212456, A212457, A212458, A212459, A212461, A212462.

Programs

  • Derive
    PROG(y := [], x := 100, LOOP(IF(x = 0, RETURN y), y := ADJOIN(CEILING(3·x·LOG(3·x)), y), x := x - 1))
  • Magma
    [Ceiling(3*n*Log(3*n)): n in [1..80]]; // Vincenzo Librandi, Feb 13 2013
  • Mathematica
    Table[Ceiling[3*n*Log[3*n]], {n, 80}] (* Vincenzo Liobrandi, Feb 13 2013 *)
  • PARI
    a(n) = ceil(3*n*log(3*n)); \\ Michel Marcus, Jan 11 2016

Formula

a(n) = A050502(3*n). - Michel Marcus, Jan 11 2016

A212461 a(n) = ceiling(4n*log(4n)).

Original entry on oeis.org

6, 17, 30, 45, 60, 77, 94, 111, 130, 148, 167, 186, 206, 226, 246, 267, 287, 308, 330, 351, 373, 395, 417, 439, 461, 484, 506, 529, 552, 575, 598, 622, 645, 669, 692, 716, 740, 764, 788, 813, 837, 861, 886, 911, 935
Offset: 1

Views

Author

Mohammad K. Azarian, May 31 2012

Keywords

Links

Crossrefs

Cf. A050502, A050504, A212455, A212456, A212457, A212458, A212459, A212460, A212462.

Programs

  • Derive
    PROG(y := [], x := 100, LOOP(IF(x = 0, RETURN y), y := ADJOIN(CEILING(4·x·LOG(4·x)), y), x := x - 1))
  • Magma
    [Ceiling(4*n*Log(4*n)): n in [1..80]]; // Vincenzo Librandi, Feb 13 2013
  • Mathematica
    Table[Ceiling[4*n*Log[4*n]], {n, 80}] (* Vincenzo Librandi, Feb 13 2013 *)
  • PARI
    a(n) = ceil(4*n*log(4*n)); \\ Michel Marcus, Jan 11 2016

Formula

a(n) = A050502(4*n). - Michel Marcus, Jan 11 2016

A212462 a(n) = ceiling(5n*log(5n)).

Original entry on oeis.org

9, 24, 41, 60, 81, 103, 125, 148, 172, 196, 221, 246, 272, 298, 324, 351, 378, 405, 433, 461, 489, 518, 546, 575, 604, 633, 663, 692, 722, 752, 782, 813, 843, 874, 904, 935, 966, 997, 1029, 1060, 1092, 1123, 1155
Offset: 1

Views

Author

Mohammad K. Azarian, May 31 2012

Keywords

Links

Crossrefs

Cf. A050502, A050504, A212455, A212456, A212457, A212458, A212459, A212460, A212461.

Programs

  • Derive
    PROG(y := [], x := 100, LOOP(IF(x = 0, RETURN y), y := ADJOIN(CEILING(5·x·LOG(5·x)), y), x := x - 1))
  • Magma
    [Ceiling(5*n*Log(5*n)): n in [1..80]]; // Vincenzo Librandi, Feb 14 2013
  • Mathematica
    Table[Ceiling[5*n*Log[5*n]], {n, 80}] (* Vincenzo Librandi, Feb 14 2013 *)
  • PARI
    a(n) = ceil(5*n*log(5*n)); \\ Michel Marcus, Jan 11 2016

Formula

a(n) = A050502(5*n). - Michel Marcus, Jan 11 2016

A050503 Nearest integer to n*log(n).

Original entry on oeis.org

0, 1, 3, 6, 8, 11, 14, 17, 20, 23, 26, 30, 33, 37, 41, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 85, 89, 93, 98, 102, 106, 111, 115, 120, 124, 129, 134, 138, 143, 148, 152, 157, 162, 167, 171, 176, 181, 186, 191, 196, 201, 205, 210, 215, 220, 225, 230, 236, 241
Offset: 1

Views

Author

N. J. A. Sloane, Dec 27 1999

Keywords

Comments

The prime number theorem states that the n-th prime is asymptotic to n*log(n).

References

  • G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Theorem 8.

Crossrefs

Cf. A000040, A050502, A050504.

Programs

  • Mathematica
    Table[Round[n Log[n]],{n,100}] (* Harvey P. Dale, Sep 27 2023 *)
Showing 1-10 of 20 results. Next

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

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