A186153 -id:A186153 - cp's OEIS frontend

A186152 Rank of (1/8)n^3 when {(1/8)i^3: i>=1} and {j^2>: j>=1} are jointly ranked with (1/8)i^3 before j^2 when (1/8)i^3=j^2. Complement of A186153.

1, 2, 4, 6, 8, 11, 13, 15, 18, 21, 23, 26, 29, 32, 35, 38, 41, 44, 48, 51, 55, 58, 61, 65, 69, 72, 76, 80, 84, 88, 92, 95, 100, 104, 108, 112, 116, 120, 125, 129, 133, 138, 142, 147, 151, 156, 160, 165, 170, 174, 179, 184, 189, 194, 199, 204, 209, 214, 219, 224, 229, 234, 239, 245, 250, 255, 260, 266, 271, 277, 282, 287, 293, 299, 304, 310, 315, 321, 327, 332, 338, 344, 350, 356, 362, 367, 373, 379, 385, 391, 397, 403, 410, 416, 422, 428, 434, 440, 447, 453

Offset: 1

Clark Kimberling, Feb 13 2011

nonn

See A186145 for a discussion of adjusted joint rank sequences.

Cf. A186145, A186153.

d=1/16;u=1/8;v=1;p=3;q=2;
h[n_]:=((u*n^p-d)/v)^(1/q);
a[n_]:=n+Floor[h[n]]; (* rank of u*n^p *)
k[n_]:=((v*n^q+d)/u)^(1/p);
b[n_]:=n+Floor[k[n]]; (* rank of v*n^q *)
Table[a[n],{n,1,100}] (* A186152 *)
Table[b[n],{n,1,100}]  (* A186153 *)

a(n)=n+floor(((1/8)n^3-1/16)^(1/2)), A186152.

b(n)=n+floor(((n^2)/16+1/2)^(1/3)), A186153.

A186155 Rank of n^2 when {(1/8)i^3: i>=1} and {j^2>: j>=1} are jointly ranked with (1/8)i^3 after j^2 when (1/8)i^3=j^2. Complement of A186154.

Original entry on oeis.org

2, 5, 7, 9, 10, 12, 14, 15, 17, 19, 20, 22, 24, 25, 27, 28, 30, 31, 33, 34, 36, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 52, 53, 54, 56, 57, 59, 60, 62, 63, 64, 66, 67, 68, 70, 71, 73, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 98, 99, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113, 114, 115, 117, 118, 119, 121, 122, 123, 124, 126, 127, 128, 130

Offset: 1

Clark Kimberling, Feb 13 2011

nonn

See A186154.

Cf. A185145, A186154, A186152, A186153.

Mathematica
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(See A186154.)
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cp's OEIS Frontend

A186152 Rank of (1/8)n^3 when {(1/8)i^3: i>=1} and {j^2>: j>=1} are jointly ranked with (1/8)i^3 before j^2 when (1/8)i^3=j^2. Complement of A186153.

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