login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A101993 A002481 A183870 * A193627 A256792 A085817

Adjacent sequences:  A186494 A186495 A186496 * A186498 A186499 A186500

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 22 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 12 22:06 EST 2019. Contains 329963 sequences. (Running on oeis4.)