A186222 Adjusted joint rank sequence of (g(i)) and (f(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the triangular numbers and squares. Complement of A186221.

1, 4, 6, 9, 11, 13, 16, 18, 21, 23, 26, 28, 30, 33, 35, 38, 40, 42, 45, 47, 50, 52, 55, 57, 59, 62, 64, 67, 69, 71, 74, 76, 79, 81, 83, 86, 88, 91, 93, 96, 98, 100, 103, 105, 108, 110, 112, 115, 117, 120, 122, 125, 127, 129, 132, 134, 137, 139, 141, 144, 146, 149, 151, 154, 156, 158, 161, 163, 166, 168, 170, 173, 175, 178, 180, 182, 185, 187, 190, 192, 195, 197, 199, 202, 204, 207, 209, 211, 214, 216, 219, 221, 224, 226, 228, 231, 233, 236, 238, 240

Offset: 1

Author

Clark Kimberling, Feb 15 2011

Keywords

• nonn

Comments

See A186221.

Examples

			See A186221.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A186219, A186220, A186221.

Programs

Magma

[n + Floor(-1/2 + Sqrt(2*n^2)): n in [1..120]]; // G. C. Greubel, Aug 18 2018

Mathematica

(* adjusted joint ranking; general formula *)
d=-1/4; u=1/2; v=1/2; w=0; x=1; y=0; 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}] (* A186221 *)
Table[b[n],{n,1,100}] (* A186222 *)
Table[n + Floor[Sqrt[2*n^2] - 1/2], {n, 1, 120}] (* G. C. Greubel, Aug 18 2018 *)

PARI

vector(120, n, n + floor(-1/2 + sqrt(2*n^2))) \\ G. C. Greubel, Aug 18 2018

Formula

a(n) = n + floor(-1/2 + sqrt(2*n^2)).