A186320 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 heptagonal numbers. Complement of A186321.

1, 3, 5, 6, 8, 10, 11, 13, 14, 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, 125, 127, 129, 130, 132, 134, 135, 137, 139, 140, 142, 143, 145, 147, 148, 150, 152, 153, 155, 157, 158, 160, 161, 163

Offset

1,2

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 before the heptagonal:
a=(1,3,5,6,8,10,11,13,...)=A186320
b=(2,4,7,9,12,15,17,20,...)=A186321.

Mathematica

(* adjusted joint ranking; general formula *)
d=1/2; u=1; v=0; 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}]  (* A186320 *)
Table[b[n], {n, 1, 100}]  (* A186321 *)

Crossrefs

Cf. A186219, A186321, A186322, A186323,

A000290 (squares), A000566 (heptagonal numbers).

Sequence in context: A184582 A184734 A189662 * A247913 A188046 A244644

Adjacent sequences: A186317 A186318 A186319 * A186321 A186322 A186323

Keyword

nonn

Author

Clark Kimberling, Feb 17 2011

Status

approved