proposed

approved

editing

proposed

Sean A. Irvine, <a href="/A186542/b186542.txt">Table of n, a(n) for n = 1..10000</a>

approved

editing

_Clark Kimberling (ck6(AT)evansville.edu), _, Feb 23 2011

proposed

approved

allocated for Clark KimberlingAdjusted 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)=-2+3j^2. Complement of A186541.

1, 5, 7, 10, 13, 16, 19, 21, 24, 27, 29, 32, 35, 38, 40, 43, 46, 49, 51, 54, 57, 60, 62, 65, 68, 71, 73, 76, 79, 81, 84, 87, 90, 92, 95, 98, 101, 103, 106, 109, 111, 114, 117, 120, 122, 125, 128, 131, 133, 136, 139, 142, 144, 147, 150, 152, 155, 158, 161, 163, 166, 169, 172, 174, 177, 180, 183, 185, 188, 191, 193, 196, 199, 202, 204, 207, 210, 213, 215, 218, 221, 224, 226, 229, 232, 234, 237, 240

1,2

See A186219 for a discussion of adjusted joint rank sequences.

a(n)=n+floor(sqrt((1/3)n^2+5/6))=A186541(n).

b(n)=n+floor(sqrt(3n^2-5/2))=A186542(n).

First, write

1..4..9..16..25..36..49..... (i^2)

.........10.....25.....46.. (-2+3j^2)

Then replace each number by its rank, where ties are settled by ranking i^2 after -2+3j^2:

a=(2,3,4,6,8,9,11,12,14,15,17,18,..)=A186541

b=(1,5,7,10,13,16,19,21,24,27,29...)=A186542.

(See A186541.)

Cf. A186219, A186539, A186540, A186541.

allocated

nonn

Clark Kimberling (ck6(AT)evansville.edu), Feb 23 2011

approved

proposed

allocated for Clark Kimberling

allocated

approved