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 15 results. Next

A135660 a(n) = ceiling(sqrt(n) - n^(1/3)).

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
Offset: 1

Views

Author

Mohammad K. Azarian, Nov 25 2007

Keywords

Links

Crossrefs

Cf. A000196, A048766, A134914.

Programs

  • Magma
    [Ceiling(n^(1/2) - n^(1/3)): n in [1..100]]; // Vincenzo Librandi, Feb 16 2013
  • Mathematica
    Table[Ceiling[n^(1/2) - n^(1/3)], {n, 100}] (* Vincenzo Librandi, Feb 16 2013 *)

Extensions

Changed offset from 2 to 1 by Vincenzo Librandi, Feb 16 2013

A135661 a(n) = floor(sqrt(n) - n^(1/3)).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
Offset: 1

Views

Author

Mohammad K. Azarian, Nov 25 2007

Keywords

Links

Crossrefs

Cf. A000196, A048766, A134914, A135660.

Programs

  • Magma
    [Floor(n^(1/2)-n^(1/3)): n in [1..100]]; // Vincenzo Librandi, Feb 18 2013
  • Mathematica
    Table[Floor[n^(1/2) - n^(1/3)], {n, 100}] (* Vincenzo Librandi, Feb 18 2013 *)

Extensions

Offset corrected by M. F. Hasler, Nov 17 2008

A135662 a(n) = ceiling(sqrt(n) - n^(1/4)).

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
Offset: 1

Views

Author

Mohammad K. Azarian, Nov 25 2007

Keywords

Links

Crossrefs

Cf. A000196, A048766, A134914, A135660, A135661.

Programs

  • Magma
    [Ceiling(n^(1/2) - n^(1/4)): n in [1..100]]; // Vincenzo Librandi, Feb 16 2013
  • Mathematica
    Table[Ceiling[n^(1/2) - n^(1/4)], {n, 100}] (* Vincenzo Librandi, Feb 16 2013 *)

Extensions

Offset corrected by M. F. Hasler, Nov 17 2008

A135663 a(n) = floor(sqrt(n) - n^(1/4)).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7
Offset: 1

Views

Author

Mohammad K. Azarian, Nov 25 2007

Keywords

Links

Crossrefs

Cf. A000196, A048766, A134914, A135660, A135661, A135662.

Programs

  • Magma
    [Floor(n^(1/2)-n^(1/4)): n in [1..100]]; // Vincenzo Librandi, Feb 18 2013
  • Mathematica
    Table[Floor[n^(1/2) - n^(1/4)], {n, 100}] (* Vincenzo Librandi, Feb 18 2013 *)

Extensions

More terms from N. J. A. Sloane, Aug 08 2008
Offset changed from 0 to 1 by Vincenzo Librandi, Feb 18 2013

A135668 a(n) = ceiling(n + sqrt(n)).

Original entry on oeis.org

2, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67
Offset: 1

Views

Author

Mohammad K. Azarian, Nov 25 2007

Keywords

Comments

Complement of A002061. - Kieren MacMillan, Dec 16 2007

Links

Crossrefs

Cf. A134914, A135660, A135661, A135662, A135663, A135664, A135665, A028391, A002061.

Programs

  • Magma
    [Ceiling(n + n^(1/2)): n in [1..100]]; // Vincenzo Librandi, Feb 16 2013
  • Mathematica
    Table[Ceiling[n + n^(1/2)], {n, 100}] (* Vincenzo Librandi, Feb 16 2013 *)
  • Python
    from sympy import integer_nthroot
def A135668(n): return n+(a:=integer_nthroot(n,2))[0]+(not a[1]) # Chai Wah Wu, Aug 26 2024

A135664 a(n) = ceiling(sqrt(n) - n^(1/5)).

Original entry on oeis.org

0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7
Offset: 1

Views

Author

Mohammad K. Azarian, Nov 25 2007

Keywords

Links

Crossrefs

Cf. A000196, A048766, A134914, A135660, A135661, A135662, A135663.

Programs

  • Magma
    [Ceiling(n^(1/2) - n^(1/5)): n in [1..100]]; // Vincenzo Librandi, Feb 16 2013
  • Mathematica
    Table[Ceiling[n^(1/2) - n^(1/5)], {n, 100}] (* Vincenzo Librandi, Feb 16 2013 *)

Extensions

Offset corrected by Mohammad K. Azarian, Nov 19 2008

A135665 a(n) = floor(sqrt(n) - n^(1/5)).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6
Offset: 1

Views

Author

Mohammad K. Azarian, Nov 25 2007

Keywords

Links

Crossrefs

Cf. A000196, A048766, A134914, A135660, A135661, A135662, A135663, A135664.

Programs

  • Magma
    [Floor(n^(1/2)-n^(1/5)): n in [1..100]]; // Vincenzo Librandi, Feb 18 2013
  • Mathematica
    Table[Floor[n^(1/2) - n^(1/5)], {n, 100}] (* Vincenzo Librandi, Feb 18 2013 *)

Extensions

Offset corrected by Mohammad K. Azarian, Nov 19 2008

A214079 a(n) = ceiling( n^(1/3) )!.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 120, 120, 120, 120, 120
Offset: 0

Views

Author

Mohammad K. Azarian, Dec 22 2012

Keywords

Links

Crossrefs

Cf. A214078, A214079, A214080, A214081, A214083, A055228, A055226.
Cf. A000142, A134914.

Programs

  • Derive
    PROG(y := [], x := 70, LOOP(IF(x = -1, RETURN y), y := ADJOIN(CEILING(x^(1/3))!, y), x := x - 1))
  • Magma
    [Factorial(Ceiling(n^(1/3))): n in [0..80]]; // Vincenzo Librandi, Feb 13 2013
  • Mathematica
    Table[Ceiling[n^(1/3)]!, {n, 0, 100}] (* T. D. Noe, Dec 23 2012 *)
Ceiling[Surd[Range[0,70],3]]! (* Harvey P. Dale, Nov 19 2022 *)
  • PARI
    a(n) = ceil(n^(1/3))! \\ Altug Alkan, Jan 11 2016

Formula

Sum_{n>=0} 1/a(n) = 4*e. - Amiram Eldar, Aug 15 2022
a(n) = A000142(A134914(n)). - Michel Marcus, Aug 15 2022

A134917 a(n) = ceiling(n^(4/3)).

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 14, 16, 19, 22, 25, 28, 31, 34, 37, 41, 44, 48, 51, 55, 58, 62, 66, 70, 74, 78, 81, 86, 90, 94, 98, 102, 106, 111, 115, 119, 124, 128, 133, 137, 142, 146, 151, 156, 161, 165, 170, 175, 180, 185, 190, 195, 200
Offset: 1

Views

Author

Mohammad K. Azarian, Nov 17 2007

Keywords

Links

Crossrefs

Cf. A048766, A038605, A003059, A134914, A129011, A100196, A121536.

Programs

A134918 Ceiling(n^(5/3)).

Original entry on oeis.org

1, 4, 7, 11, 15, 20, 26, 32, 39, 47, 55, 63, 72, 82, 92, 102, 113, 124, 136, 148, 160, 173, 187, 200, 214, 229, 243, 259, 274, 290, 306, 323, 340, 357, 375, 393, 411, 430, 449, 468, 488, 508, 528, 549, 570, 591, 613, 634, 657
Offset: 1

Views

Author

Mohammad K. Azarian, Nov 17 2007

Keywords

Links

Crossrefs

Cf. A048766, A038605, A003059, A134914, A129011, A100196, A121536, A134917.

Programs

Showing 1-10 of 15 results. Next

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

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