A186512 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)=-4+5j^2. Complement of A186511.

1, 5, 9, 12, 15, 19, 22, 25, 29, 32, 35, 38, 41, 45, 48, 51, 54, 58, 61, 64, 67, 71, 74, 77, 80, 84, 87, 90, 93, 97, 100, 103, 106, 109, 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

1,2

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-1),F(2h-1)), where L=A000032 (Lucas numbers) and F=A000045 (Fibonacci numbers).

Links

Table of n, a(n) for n=1..82.

Formula

a(n)=n+floor(sqrt((n^2)/5+9/10))=A186511(n).

b(n)=n+floor(sqrt(5n^2-9/2))=A186512(n).

Example

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 after -4+5j^2:
a=(2,3,4,6,7,8,10,11,13,14,16,...)=A186511
b=(1,5,9,12,15,19,22,25,29,32,...)=A186512.

Mathematica

(See A186511.)

Crossrefs

Cf. A186219, A186499, A186500, A186511.

Sequence in context: A314615 A314616 A141292 * A314617 A068477 A314618

Adjacent sequences: A186509 A186510 A186511 * A186513 A186514 A186515

Keyword

nonn

Author

Clark Kimberling, Feb 22 2011

Status

approved