A186514 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 A186513.

4, 6, 10, 13, 16, 19, 22, 26, 29, 32, 35, 38, 42, 45, 48, 51, 55, 58, 61, 64, 68, 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, 178, 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

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..82.

Formula

a(n)=n+floor((1/10)(-4+sqrt(20n^2+6)))=A186513(n).

b(n)=n+floor(sqrt(5n^2+4n+1/2))=A186514(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 before 4+5j^2:
a=(1,2,3,5,7,8,9,11,12,14,15,17,..)=A186513
b=(4,6,10,13,16,19,22,26,29,32,...)=A186514.

Mathematica

(See A186513.)

Crossrefs

Cf. A186219, A186513, A186515, A186516.

Sequence in context: A224796 A190370 A246439 * A184402 A350567 A079524

Adjacent sequences: A186511 A186512 A186513 * A186515 A186516 A186517

Keyword

nonn

Author

Clark Kimberling, Feb 22 2011

Status

approved