A186322 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 heptagonal numbers. Complement of A186323.

2, 3, 5, 6, 8, 10, 11, 13, 15, 16, 18, 19, 21, 23, 24, 26, 28, 29, 31, 32, 34, 36, 37, 39, 41, 42, 44, 46, 47, 49, 50, 52, 54, 55, 57, 59, 60, 62, 63, 65, 67, 68, 70, 72, 73, 75, 77, 78, 80, 81, 83, 85, 86, 88, 90, 91, 93, 94, 96, 98, 99, 101, 103, 104, 106, 108, 109, 111, 112, 114, 116, 117, 119, 121, 122, 124, 126, 127, 129, 130, 132, 134, 135, 137, 139, 140, 142, 143, 145, 147, 148, 150, 152, 153, 155, 157, 158, 160, 161, 163

Offset

1,1

Links

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

Example

First, write
1..4...9..16....25...36...49...64.. (squares)
1....7.......18....34........55.... (heptagonal)
Replace each number by its rank, where ties are settled by ranking the square number after the heptagonal:
a=(2,3,5,6,8,10,11,13,...)=A186322
b=(1,4,7,9,12,15,17,20,...)=A186323.

Mathematica

(* adjusted joint ranking; general formula *)
d=-1/2; u=1; v=0; w=0; x=2; y=-1; 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}]  (* A186322 *)
Table[b[n], {n, 1, 100}]  (* A186323 *)

Crossrefs

Cf. A186219, A186320, A186321, A186323.

Sequence in context: A026355 A099267 A007067 * A092979 A135260 A248560

Adjacent sequences: A186319 A186320 A186321 * A186323 A186324 A186325

Keyword

nonn

Author

Clark Kimberling, Feb 17 2011

Status

approved