A186384 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=5i and g(j)=j(j+1)/2 (triangular number). Complement of A186383.

1, 2, 4, 6, 8, 10, 12, 15, 18, 21, 24, 27, 31, 35, 39, 43, 47, 52, 57, 62, 67, 72, 78, 84, 90, 96, 102, 109, 116, 123, 130, 137, 145, 153, 161, 169, 177, 186, 195, 204, 213, 222, 232, 242, 252, 262, 272, 283, 294, 305, 316, 327, 339, 351, 363, 375, 387, 400, 413, 426, 439, 452, 466, 480, 494, 508, 522, 537, 552, 567, 582, 597, 613, 629, 645, 661, 677, 694, 711, 728, 745, 762, 780, 798, 816, 834, 852, 871, 890

Offset: 1

Author

Clark Kimberling, Feb 19 2011

Keywords

• nonn

Examples

			First, write
.....5...10..15..20..25..30.. (5i)
1..3..6..10..15....21..28.. (triangular)
Then replace each number by its rank, where ties are settled by ranking 5i before the triangular:
a=(3,5,7,9,11,13,14,16,17,..)=A186383
b=(1,2,4,6,8,10,12,15,18,...)=A186384.
		

Crossrefs

Cf. A186350, A186383, A186385, A186386.

Programs

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}]  (* A186383 *)
Table[b[n], {n, 1, 100}]  (* A186384 *)