A186542 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=-2+3j^2. Complement of A186541.

1, 5, 7, 10, 13, 16, 19, 21, 24, 27, 29, 32, 35, 38, 40, 43, 46, 49, 51, 54, 57, 60, 62, 65, 68, 71, 73, 76, 79, 81, 84, 87, 90, 92, 95, 98, 101, 103, 106, 109, 111, 114, 117, 120, 122, 125, 128, 131, 133, 136, 139, 142, 144, 147, 150, 152, 155, 158, 161, 163, 166, 169, 172, 174, 177, 180, 183, 185, 188, 191, 193, 196, 199, 202, 204, 207, 210, 213, 215, 218, 221, 224, 226, 229, 232, 234, 237, 240

Offset

1,2

Comments

See A186219 for a discussion of adjusted joint rank sequences.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Formula

a(n)=n+floor(sqrt((1/3)n^2+5/6))=A186541(n).

b(n)=n+floor(sqrt(3n^2-5/2))=A186542(n).

Example

First, write
1..4..9..16..25..36..49..... (i^2)
.........10.....25.....46.. (-2+3j^2)
Then replace each number by its rank, where ties are settled by ranking i^2 after -2+3j^2:
a=(2,3,4,6,8,9,11,12,14,15,17,18,..)=A186541
b=(1,5,7,10,13,16,19,21,24,27,29...)=A186542.

Mathematica

(See A186541.)

Crossrefs

Cf. A186219, A186539, A186540, A186541.

Sequence in context: A179196 A024325 A060873 * A287444 A196175 A112251

Adjacent sequences: A186539 A186540 A186541 * A186543 A186544 A186545

Keyword

nonn

Author

Clark Kimberling, Feb 23 2011

Status

approved