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A186500 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 A186499. 6
2, 6, 9, 12, 16, 19, 22, 25, 29, 32, 35, 38, 42, 45, 48, 51, 54, 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, 232, 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-2),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((1/10)(sqrt(2n^2+7)))=A186499(n).

b(n)=n+floor(sqrt(5n^2-7/2))=A186500(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 before -4+5j^2:

a=(1,3,4,5,7,8,10,11,13,14,15,17,18...)=A186499

b=(2,6,9,12,16,19,22,25,29,32,35,38,.)=A186500.

MATHEMATICA

(See A186499.)

CROSSREFS

Cf. A186219, A186499, A186511, A186512.

Sequence in context: A190059 A190332 A187912 * A190777 A184619 A184119

Adjacent sequences:  A186497 A186498 A186499 * A186501 A186502 A186503

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 22 2011

STATUS

approved

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Last modified August 1 06:45 EDT 2021. Contains 346384 sequences. (Running on oeis4.)