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

1,2

Links

Table of n, a(n) for n=1..89.

Example

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.

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 *)

Crossrefs

Cf. A186350, A186383, A186385, A186386.

Sequence in context: A278453 A347009 A130261 * A011860 A259278 A049445

Adjacent sequences: A186381 A186382 A186383 * A186385 A186386 A186387

Keyword

nonn

Author

Clark Kimberling, Feb 19 2011

Status

approved