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A186324 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the squares and octagonal numbers. Complement of A186325. 4
1, 3, 5, 6, 8, 9, 11, 12, 14, 16, 17, 19, 20, 22, 23, 25, 27, 28, 30, 31, 33, 35, 36, 38, 39, 41, 42, 44, 46, 47, 49, 50, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 69, 71, 72, 74, 76, 77, 79, 80, 82, 83, 85, 87, 88, 90, 91, 93, 94, 96, 98, 99, 101, 102, 104, 106, 107, 109, 110, 112, 113, 115, 117, 118, 120, 121, 123, 124, 126, 128, 129, 131, 132, 134, 135, 137, 139, 140, 142, 143, 145, 147, 148, 150, 151, 153, 154, 156, 158 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
See A186219 for a discussion of adjusted joint rank sequences.
LINKS
EXAMPLE
First, write
1..4...9..16....25..36....49..64... (squares)
1....8.......21........40........65. (octagonal)
Replace each number by its rank, where ties are settled by ranking the square number before the octagonal:
a=(1,3,5,6,8,9,11,12,14,...)=A186324
b=(2,4,7,10,13,15,18,21,...)=A186325.
MATHEMATICA
(* adjusted joint ranking; general formula *)
d=1/2; u=1; v=0; w=0; x=3; y=-2; z=0;
h[n_]:=-y+(4x(u*n^2+v*n+w-z-d)+y^2)^(1/2);
a[n_]:=n+Floor[h[n]/(2x)];
k[n_]:=-v+(4u(x*n^2+y*n+z-w+d)+v^2)^(1/2);
b[n_]:=n+Floor[k[n]/(2u)];
Table[a[n], {n, 1, 100}] (* A186324 *)
Table[b[n], {n, 1, 100}] (* A186325 *)
CROSSREFS
A000290 (squares), A000567 (octagonal).
Sequence in context: A336410 A121506 A114119 * A101358 A276210 A186223
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 17 2011
STATUS
approved

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Last modified February 23 02:51 EST 2024. Contains 370265 sequences. (Running on oeis4.)