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A186317 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 hexagonal numbers.  Complement of A186318. 4
2, 3, 5, 7, 8, 10, 12, 13, 15, 17, 19, 20, 22, 24, 25, 27, 29, 30, 32, 34, 36, 37, 39, 41, 42, 44, 46, 48, 49, 51, 53, 54, 56, 58, 60, 61, 63, 65, 66, 68, 70, 71, 73, 75, 77, 78, 80, 82, 83, 85, 87, 89, 90, 92, 94, 95, 97, 99, 100, 102, 104, 106, 107, 109, 111, 112, 114, 116, 118, 119, 121, 123, 124, 126, 128, 129, 131, 133, 135, 136, 138, 140, 141, 143, 145, 147, 148, 150, 152, 153, 155, 157, 159, 160, 162, 164, 165, 167, 169, 170 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

First, write

1..4...9...16..25....36....49. (squares)

1....6...15.......28....45.... (hexagonals)

Replace each number by its rank, where ties are settled by ranking the square number after the hexagonal:

a=(2,3,5,7,8,10,12,13,...)=A186317.

b=(1,4,6,9,11,14,16,18,...)=A186318.

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}]  (* A186317 *)

Table[b[n], {n, 1, 100}]  (* A186318 *)

CROSSREFS

Cf. A186315, A186316, A186318.

Sequence in context: A028763 A285977 A186344 * A285077 A143826 A001912

Adjacent sequences:  A186314 A186315 A186316 * A186318 A186319 A186320

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 17 2011

STATUS

approved

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Last modified January 18 20:19 EST 2018. Contains 297865 sequences.