A135674 -id:A135674 - cp's OEIS frontend

A186147 Rank of n^3 when {i^2: i>=1} and {j^3: j>=1} are jointly ranked with i^2 after j^3 when i^2=j^3. Complement of A135674.

1, 4, 8, 11, 16, 20, 25, 30, 35, 41, 47, 53, 59, 66, 73, 79, 87, 94, 101, 109, 117, 125, 133, 141, 149, 158, 167, 176, 185, 194, 203, 213, 222, 232, 242, 251, 262, 272, 282, 292, 303, 314, 324, 335, 346, 357, 369, 380, 391, 403, 415, 426, 438, 450, 462, 475, 487, 499, 512, 524, 537, 550, 563, 575, 589, 602, 615, 628, 642, 655, 669, 682, 696, 710, 724, 738, 752, 766, 781, 795, 809, 824, 839, 853, 868, 883, 898, 913

Offset: 1

Clark Kimberling, Feb 13 2011

nonn

See A186145.

Cf. A135674, A186145.

d=-1/2;
a[n_]:=n+Floor[(n^2-d)^(1/3)]; (* rank of n^2 *)
b[n_]:=n+Floor[(n^3+d)^(1/2)]; (* rank of n^3-1/2 *)
Table[a[n],{n,1,100}]  (* A135674 *)
Table[b[n],{n,1,100}]  (* A186147 *)

b(n):=n+floor((n^3-1/2)^(1/2)), as in the Mathematica program.

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 *)

A135678 Floor(n^(4/3)+n).

Original entry on oeis.org

2, 4, 7, 10, 13, 16, 20, 24, 27, 31, 35, 39, 43, 47, 51, 56, 60, 65, 69, 74, 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 138, 144, 149, 154, 160, 165, 171, 176, 182, 187, 193, 199, 205, 210, 216, 222, 228, 234, 240

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; A135677.

[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 *)

cp's OEIS Frontend

A186147 Rank of n^3 when {i^2: i>=1} and {j^3: j>=1} are jointly ranked with i^2 after j^3 when i^2=j^3. Complement of A135674.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Extensions

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

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions

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

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

A135678 Floor(n^(4/3)+n).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica