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.
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
Offset: 1
Keywords
Examples
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.
Programs
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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 *)
Comments