A186497 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=3i-2 and g(j)=j-th triangular number. Complement of A186498.

1, 4, 6, 7, 9, 11, 12, 14, 15, 16, 18, 19, 21, 22, 23, 25, 26, 27, 28, 30, 31, 32, 34, 35, 36, 37, 39, 40, 41, 42, 43, 45, 46, 47, 48, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 105, 106, 108, 109, 110, 111, 112, 113, 114, 116, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146

Offset

1,2

Comments

See A186350 for a discussion of adjusted joint rank sequences.

Links

Table of n, a(n) for n=1..120.

Example

First, write
1..4..7.10..13..16..19..22..25..28..31. (3i-2),
1.3..6..10....15.......21.......28.....(j(j+1)/2).
Then replace each number by its rank, where ties are settled by ranking 3i-2 before j(j+1)/2:
a=(1,4,6,7,9,11,12,14,15,16,18,...)=A186497,
b=(2,3,5,8,10,13,17,20,24,29,33,..)=A186498.

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=3; v=-2; x=1/2; 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}]  (* A186497 *)
Table[b[n], {n, 1, 100}]  (* A186498 *)

Crossrefs

Cf. A186350, A186498, A186499, A186500.

Sequence in context: A002481 A370268 A183870 * A193627 A256792 A367186

Adjacent sequences: A186494 A186495 A186496 * A186498 A186499 A186500

Keyword

nonn

Author

Clark Kimberling, Feb 22 2011

Status

approved