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A186148
Rank of (1/4)n^3 when {(1/4)i^3: i>=1} and {j^2>: j>=1} are jointly ranked with (1/4)i^3 before j^2 when (1/4)i^3=j^2. Complement of A186149.
3
1, 3, 5, 7, 10, 13, 16, 19, 22, 25, 29, 32, 36, 40, 44, 47, 52, 56, 60, 64, 69, 73, 78, 82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 133, 138, 143, 149, 155, 160, 166, 172, 178, 183, 189, 195, 201, 208, 214, 220, 226, 233, 239, 245, 252, 258, 265, 272, 278, 285, 292, 299, 306, 313, 319, 327, 334, 341, 348, 355, 362, 370, 377, 384, 392, 399, 407, 414, 422, 430, 437, 445, 453, 461, 468, 476, 484, 492, 500
OFFSET
1,2
COMMENTS
See A187645.
FORMULA
a(n) = n + floor(((1/4)*n^3 - 1/8)^(1/2)).
EXAMPLE
Write preliminary separate rankings:
1/4...2....27/4....16.....125/4...
....1...4.......9..16..25........36..49
Then replace each number by its rank, where ties are settled by ranking the top number before the bottom.
MATHEMATICA
d=1/8; u=1/4; 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}] (* A186148 *)
Table[b[n], {n, 1, 100}] (* A186149 *)
CROSSREFS
Sequence in context: A213510 A130257 A276498 * A079511 A092757 A062430
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 13 2011
STATUS
approved