A135663 -id:A135663 - cp's OEIS frontend

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

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

Mohammad K. Azarian, Nov 25 2007

Complement of A002061. - Kieren MacMillan, Dec 16 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

[Ceiling(n + n^(1/2)): n in [1..100]]; // Vincenzo Librandi, Feb 16 2013

Table[Ceiling[n + n^(1/2)], {n, 100}] (* Vincenzo Librandi, Feb 16 2013 *)

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

Mohammad K. Azarian, Nov 25 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

[Ceiling(n^(1/2) - n^(1/5)): n in [1..100]]; // Vincenzo Librandi, Feb 16 2013

Table[Ceiling[n^(1/2) - n^(1/5)], {n, 100}] (* Vincenzo Librandi, Feb 16 2013 *)

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

Mohammad K. Azarian, Nov 25 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

[Floor(n^(1/2)-n^(1/5)): n in [1..100]]; // Vincenzo Librandi, Feb 18 2013

Table[Floor[n^(1/2) - n^(1/5)], {n, 100}] (* Vincenzo Librandi, Feb 18 2013 *)

Offset corrected by Mohammad K. Azarian, Nov 19 2008

A135671 a(n) = ceiling(n - n^(2/3)).

Original entry on oeis.org

0, 1, 1, 2, 3, 3, 4, 4, 5, 6, 7, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 22, 22, 23, 24, 25, 26, 26, 27, 28, 29, 30, 30, 31, 32, 33, 34, 34, 35, 36, 37, 38, 39, 39, 40, 41, 42, 43, 44, 44, 45, 46

Offset: 1

Mohammad K. Azarian, Nov 25 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A135660, A135661, A135662, A135663, A135664, A135665, A028391, A135668, A135669, A135670.

[Ceiling(n - n^(2/3)): n in [1..100]]; // Vincenzo Librandi, Feb 16 2013

Table[Ceiling[n - n^(2/3)], {n, 100}] (* Vincenzo Librandi, Feb 16 2013 *)

a(n)=n-sqrtnint(n^2,3) \\ Charles R Greathouse IV, Sep 02 2015

Offset corrected by Mohammad K. Azarian, Nov 19 2008

A135672 a(n) = floor(n - n^(2/3)).

Original entry on oeis.org

0, 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 14, 14, 15, 16, 17, 18, 18, 19, 20, 21, 21, 22, 23, 24, 25, 25, 26, 27, 28, 29, 29, 30, 31, 32, 33, 33, 34, 35, 36, 37, 38, 38, 39, 40, 41, 42, 43, 43, 44, 45

Offset: 1

Mohammad K. Azarian, Nov 25 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A135660, A135661, A135662, A135663, A135664, A135665, A028391, A135668, A135669, A135670, A135671.

[Floor(n-n^(2/3)): n in [1..100]]; // Vincenzo Librandi, Feb 18 2013

Table[Floor[n - n^(2/3)], {n, 100}] (* Vincenzo Librandi, Feb 18 2013 *)

a(n)=n-sqrtnint(n^2-1,3)-1 \\ Charles R Greathouse IV, Sep 02 2015

Offset corrected by Mohammad K. Azarian, Nov 19 2008

A135673 Ceiling(n + n^(2/3)).

Original entry on oeis.org

2, 4, 6, 7, 8, 10, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 24, 25, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 82, 83

Offset: 1

Mohammad K. Azarian, Nov 25 2007

			a(6) = 10; ceiling(6 + 6^(2/3)) = ceiling(9.30192...) = 10.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A135660, A135661, A135662, A135663, A135664, A135665, A028391, A135668, A135669, A135670, A135671, A135672.

[Ceiling(n + n^(2/3)): n in [1..100]]; // Vincenzo Librandi, Feb 16 2013

A135673:=n->ceil(n + n^(2/3)); seq(A135673(k), k=1..100); # Wesley Ivan Hurt, Nov 01 2013

Table[Ceiling[n+n^(2/3)],{n,60}] (* Harvey P. Dale, Nov 17 2012 *)

More terms from Wesley Ivan Hurt, Nov 01 2013

A135674 Floor(n+n^(2/3)).

Original entry on oeis.org

2, 3, 5, 6, 7, 9, 10, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 74

Offset: 1

Mohammad K. Azarian, Nov 25 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A135660, A135661, A135662, A135663, A135664, A135665, A028391, A135668, A135669, A135670, A135671, A135672, A135673.

[Floor(n+n^(2/3)): n in [1..100]]; // Vincenzo Librandi, Feb 18 2013

Table[Floor[n + n^(2/3)], {n, 100}] (* Vincenzo Librandi, Feb 18 2013 *)

A135675 a(n) = ceiling(n^(4/3) - n).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 18, 20, 22, 25, 27, 30, 32, 35, 37, 40, 43, 46, 49, 52, 54, 58, 61, 64, 67, 70, 73, 77, 80, 83, 87, 90, 94, 97, 101, 104, 108, 112, 116, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155

Offset: 1

Mohammad K. Azarian, Dec 01 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A135660, A135661, A135662, A135663, A135664, A135665, A028391, A135668, A135671, A135672, A135673, A135674.

[Ceiling(n^(4/3) - n): n in [1..100]]; // Vincenzo Librandi, Feb 16 2013

Table[Ceiling[n^(4/3) - n], {n, 100}] (* Vincenzo Librandi, Feb 16 2013 *)

Offset corrected by Mohammad K. Azarian, Nov 19 2008

A135676 a(n) = floor(n^(4/3) - n).

Original entry on oeis.org

0, 0, 1, 2, 3, 4, 6, 8, 9, 11, 13, 15, 17, 19, 21, 24, 26, 29, 31, 34, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 76, 79, 82, 86, 89, 93, 96, 100, 103, 107, 111, 115, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158

Offset: 1

Mohammad K. Azarian, Dec 01 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A135660, A135661, A135662, A135663, A135664, A135665, A028391, A135668, A135671, A135672, A135673, A135674, A135675.

[Floor(n^(4/3)-n): n in [1..100]]; // Vincenzo Librandi, Feb 18 2013

Table[Floor[n^(4/3) - n], {n, 100}] (* Vincenzo Librandi, Feb 18 2013 *)

a(n)=sqrtnint(n^4,3)-n \\ Charles R Greathouse IV, Feb 07 2025

Offset corrected by Mohammad K. Azarian, Nov 19 2008

A135677 a(n) = ceiling(n^(4/3)+n).

Original entry on oeis.org

2, 5, 8, 11, 14, 17, 21, 24, 28, 32, 36, 40, 44, 48, 52, 57, 61, 66, 70, 75, 79, 84, 89, 94, 99, 104, 108, 114, 119, 124, 129, 134, 139, 145, 150, 155, 161, 166, 172, 177, 183, 188, 194, 200, 206, 211, 217, 223, 229, 235, 241

Offset: 1

Mohammad K. Azarian, Dec 01 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A135660, A135661, A135662, A135663, A135664, A135665, A028391, A135668, A135671, A135672, A135673, A135674, A135675, A135676.

[Ceiling(n^(4/3)+n): n in [1..100]]; // Vincenzo Librandi, Feb 16 2013

Table[Ceiling[n^(4/3) + n], {n, 100}] (* Vincenzo Librandi, Feb 16 2013 *)

cp's OEIS Frontend

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

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

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

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Magma

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A135671 a(n) = ceiling(n - n^(2/3)).

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A135672 a(n) = floor(n - n^(2/3)).

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A135673 Ceiling(n + n^(2/3)).

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A135674 Floor(n+n^(2/3)).

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Magma

Mathematica

A135675 a(n) = ceiling(n^(4/3) - n).

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