A186540 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=-2+3j^2. Complement of A186539.

2, 5, 8, 10, 13, 16, 19, 21, 24, 27, 30, 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, 112, 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

Offset: 1

Author

Clark Kimberling, Feb 23 2011

Keywords

• nonn

Comments

See A186219 for a discussion of adjusted joint rank sequences.

Does this differ from A054088? The first 42000 entries of both sequences at least are the same. - R. J. Mathar, Feb 25 2011

Examples

			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 before -2+3j^2:
b=(1,3,4,6,7,9,11,12,14,15,17,18,..)=A186539
a=(2,5,8,10,13,16,19,21,24,27,30...).
		

Crossrefs

Cf. A186219, A186539, A186541, A186542.

Programs

Mathematica

(* See A186539 *)

Formula

b(n) = n+floor(sqrt((1/3)n^2+1/24)) = A186539(n).

a(n) = n+floor(sqrt(3n^2-3/2)).