A186383 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 A186384.

3, 5, 7, 9, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 30, 32, 33, 34, 36, 37, 38, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 56, 58, 59, 60, 61, 63, 64, 65, 66, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 91

Offset

1,1

Links

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

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, A186384, A186385, A186386.

Sequence in context: A231773 A007617 A065878 * A284055 A248564 A286999

Adjacent sequences: A186380 A186381 A186382 * A186384 A186385 A186386

Keyword

nonn

Author

Clark Kimberling, Feb 19 2011

Status

approved