A186389 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=6i and g(j)=j(j+1)/2 (triangular number). Complement of A186390.

4, 6, 8, 10, 12, 14, 15, 17, 18, 20, 22, 23, 25, 26, 27, 29, 30, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 58, 60, 61, 62, 63, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 77, 78, 80, 81, 82, 83, 85, 86, 87, 88, 90, 91, 92

Offset

1,1

Comments

See A186350 for a discussion of adjusted joint rank sequences.

Links

Table of n, a(n) for n=1..65.

Example

First, write
......6.....12..18....24..30. (6i)
1..3..6..10...15....21..28... (triangular)
Then replace each number by its rank, where ties are settled by ranking 6i after the triangular:
a=(4,6,8,10,12,14,15,17,...)=A186389
b=(1,2,3,5,7,9,11,13,16,...)=A186390.

Mathematica

(* adjusted joint rank sequences a and b, using general formula for ranking 1st degree u*n+v and 2nd degree x*n^2+y*n+z *)
d=-1/2; u=6; v=0; x=1/2; y=1/2; (* 6i and triangular *)
h[n_]:=(-y+(4x(u*n+v-d)+y^2)^(1/2))/(2x);
a[n_]:=n+Floor[h[n]]; (* rank of u*n+v *)
k[n_]:=(x*n^2+y*n-v+d)/u;
b[n_]:=n+Floor[k[n]]; (* rank of x*n^2+y*n+d *)
Table[a[n], {n, 1, 120}]  (* A186389 *)
Table[b[n], {n, 1, 100}]  (* A186390 *)

Crossrefs

Cf. A186350, A186387, A186388, A186390.

Sequence in context: A078941 A078942 A248419 * A039767 A176235 A201221

Adjacent sequences: A186386 A186387 A186388 * A186390 A186391 A186392

Keyword

nonn

Author

Clark Kimberling, Feb 19 2011

Status

approved