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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
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 (list; graph; refs; listen; history; text; internal format)
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 A079524 A141740

Adjacent sequences:  A186511 A186512 A186513 * A186515 A186516 A186517

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 22 2011

STATUS

approved

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Last modified May 8 13:26 EDT 2021. Contains 343666 sequences. (Running on oeis4.)