A186516 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 A186515.

3, 6, 9, 13, 16, 19, 22, 25, 29, 32, 35, 38, 42, 45, 48, 51, 55, 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, 233, 236, 239, 242, 245, 249, 252, 255, 258, 262, 265, 268, 271

Offset

1,1

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

Links

Table of n, a(n) for n=1..84.

Formula

a(n)=n+floor(sqrt((n^2)/5-7/10))=A186515(n).

b(n)=n+floor(sqrt(5n^2+7/2))=A186516(n).

Example

First, write
1..4..9..16..25..36..49.. (i^2)
......9.....24.......49.. (4+5j^2)
Then replace each number by its rank, where ties are settled by ranking i^2 after 4+5j^2:
a=(1,2,4,5,7,8,10,11,12,14,15,17,..)=A186515
b=(3,6,9,13,16,19,22,25,29,32,35,..)=A186516.

Mathematica

(See A186515.)

Crossrefs

Cf. A186219, A186513, A186514, A186515.

Sequence in context: A088364 A022853 A198264 * A059540 A190363 A059550

Adjacent sequences: A186513 A186514 A186515 * A186517 A186518 A186519

Keyword

nonn

Author

Clark Kimberling, Feb 22 2011

Status

approved