A186326 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the squares and octagonal numbers. Complement of A186327.

2, 3, 5, 6, 8, 9, 11, 12, 14, 16, 17, 19, 20, 22, 24, 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

Author

Clark Kimberling, Feb 17 2011

Keywords

• nonn

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 after the octagonal:
a=(2,3,5,6,8,9,11,12,14,...)=A186326
b=(1,4,7,10,13,15,18,21,...)=A186327.
		

Links

• Matthias Christandl, Fulvio Gesmundo, Asger Kjærulff Jensen, Border rank is not multiplicative under the tensor product, arXiv:1801.04852 [math.AG], 2018.

Crossrefs

Cf. A186219, A186324, A186325, A186327.

Programs

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}]  (* A186326 *)
Table[b[n], {n, 1, 100}]  (* A186327 *)