A186385 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=5i and g(j)=j(j+1)/2 (triangular number). Complement of A186386.

3, 6, 8, 9, 11, 13, 14, 16, 18, 19, 21, 22, 23, 25, 26, 28, 29, 30, 32, 33, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91

Offset

1,1

Links

Table of n, a(n) for n=1..66.

Example

First, write
.....5...10..15..20..25..30.. (5*i)
1..3..6..10..15....21..28.. (triangular)
Then replace each number by its rank, where ties are settled by ranking 5*i after the triangular:
a=(3,6,8,9,11,13,14,16,18,..)=A186385
b=(1,2,4,5,7,10,12,15,17,...)=A186386.

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=5; v=0; x=1/2; y=1/2; (* 5i 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}]  (* A186385 *)
Table[b[n], {n, 1, 100}]  (* A186386 *)

Crossrefs

Cf. A186350, A186383, A186384, A186386.

Sequence in context: A036558 A005870 A194461 * A335155 A231005 A231010

Adjacent sequences: A186382 A186383 A186384 * A186386 A186387 A186388

Keyword

nonn

Author

Clark Kimberling, Feb 19 2011

Status

approved