A186237 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 triangular numbers (A000217) and heptagonal numbers (A000566). Complement of A186238.

2, 3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 43, 45, 46, 48, 49, 51, 52, 54, 55, 56, 58, 59, 61, 62, 64, 65, 67, 68, 69, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 85, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 106, 107, 109, 110, 111, 113, 114, 116, 117, 119, 120, 122, 123, 124, 126, 127, 129, 130, 132, 133, 135, 136, 138, 139, 140, 142, 143, 145

Offset

1,1

Links

Table of n, a(n) for n=1..100.

Example

See A186227.

Mathematica

(* adjusted joint ranking; general formula *)
d=-1/2; u=1/2; v=1/2; w=0; x=5/2; y=-3/2; 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}] (* A186237 *)
Table[b[n], {n, 1, 100}] (* A186238 *)

Crossrefs

Cf. A000217, A000566, A186227, A186228, A186238.

Sequence in context: A292052 A347624 A187484 * A079057 A211264 A189725

Adjacent sequences: A186234 A186235 A186236 * A186238 A186239 A186240

Keyword

nonn

Author

Clark Kimberling, Feb 16 2011

Extensions

Definition corrected by Georg Fischer, Sep 24 2021

Status

approved