A186500 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)=-4+5j^2. Complement of A186499.

2, 6, 9, 12, 16, 19, 22, 25, 29, 32, 35, 38, 42, 45, 48, 51, 54, 58, 61, 64, 67, 71, 74, 77, 80, 84, 87, 90, 93, 97, 100, 103, 106, 110, 113, 116, 119, 122, 126, 129, 132, 135, 139, 142, 145, 148, 152, 155, 158, 161, 165, 168, 171, 174, 177, 181, 184, 187, 190, 194, 197, 200, 203, 207, 210, 213, 216, 220, 223, 226, 229, 232, 236, 239, 242, 245, 249, 252, 255, 258, 262, 265

Offset: 1

Author

Clark Kimberling, Feb 22 2011

Keywords

• nonn

Comments

See A186219 for a discussion of adjusted joint rank sequences.

The pairs (i,j) for which i^2=-4+5j^2 are (L(2h-2),F(2h-1)), where L=A000032 (Lucas numbers) and F=A000045 (Fibonacci numbers).

Examples

			First, write
1..4..9..16..25..36..49..... (i^2)
1........16........41........(-4+5j^2)
Then replace each number by its rank, where ties are settled by ranking i^2 before -4+5j^2:
a=(1,3,4,5,7,8,10,11,13,14,15,17,18...)=A186499
b=(2,6,9,12,16,19,22,25,29,32,35,38,.)=A186500.
		

Crossrefs

Cf. A186219, A186499, A186511, A186512.

Programs

Mathematica

(See A186499.)

Formula

a(n)=n+floor((1/10)(sqrt(2n^2+7)))=A186499(n).

b(n)=n+floor(sqrt(5n^2-7/2))=A186500(n).