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

1,2

Comments

See A186145 for a discussion of adjusted joint rank sequences.

Links

Table of n, a(n) for n=1..100.

Formula

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.

Mathematica

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 *)

Crossrefs

Cf. A186145, A186153.

Sequence in context: A022839 A193766 A262773 * A004401 A022819 A081527

Adjacent sequences: A186149 A186150 A186151 * A186153 A186154 A186155

Keyword

nonn

Author

Clark Kimberling, Feb 13 2011

Status

approved