

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.


4



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
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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)/57/10))=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



