OFFSET
1,1
EXAMPLE
First, write
...5..10..15..20..25..30..35..40... (5i),
1..5......12......22............35..(pentagonal numbers).
Then replace each number by its rank, where ties are settled by ranking 5i after the pentagonal number:
a=(3,4,6,7,9,10,12,13,14,15,17,...)=A186495,
b=(1,2,5,8,11,16,20,26,32,38,46,..)=A186496.
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=3/2; y=-1/2;
h[n_]:=(-y+(4x(u*n+v-d)+y^2)^(1/2))/(2x);
a[n_]:=n+Floor[h[n]];
k[n_]:=(x*n^2+y*n-v+d)/u;
b[n_]:=n+Floor[k[n]];
Table[a[n], {n, 1, 120}] (* A186495 *)
Table[b[n], {n, 1, 100}] (* A186496 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 22 2011
STATUS
approved