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

1,1

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

Links

Table of n, a(n) for n=1..80.

Formula

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

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

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 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...).

Mathematica

(* See A186539 *)

Crossrefs

Cf. A186219, A186539, A186541, A186542.

Sequence in context: A309095 A022843 A054088 * A059556 A248520 A247780

Adjacent sequences: A186537 A186538 A186539 * A186541 A186542 A186543

Keyword

nonn,changed

Author

Clark Kimberling, Feb 23 2011

Status

approved