|
| |
|
|
A186347
|
|
Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=8i and g(j)=j^2. Complement of A186346.
|
|
5
|
|
|
|
1, 2, 4, 6, 8, 10, 13, 16, 19, 22, 26, 30, 34, 38, 43, 48, 53, 58, 64, 70, 76, 82, 89, 96, 103, 110, 118, 126, 134, 142, 151, 160, 169, 178, 188, 198, 208, 218, 229, 240, 251, 262, 274, 286, 298, 310, 323, 336, 349, 362, 376, 390, 404, 418, 433, 448, 463, 478, 494, 510, 526, 542, 559, 576, 593, 610, 628, 646, 664, 682, 701, 720, 739, 758, 778, 798, 818, 838, 859, 880, 901, 922, 944, 966, 988, 1010
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
a(n) = a(-8-n) for all n in Z using the formula. - Michael Somos, Apr 05 2024
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n)=n+floor(sqrt(8n-1/2))=A186346(n).
b(n)=n+floor((n^2+1/2)/8)=A186347(n).
G.f.: x*(1 + x^2 - x^4)/((1 - x)^2 * (1 - x^4)). - Michael Somos, Apr 05 2024
|
|
|
EXAMPLE
|
First, write
....8....16..24..32..40..48..56..64..72..80.. (8i)
1..4..9..16...25...36......49....64.......81 (squares)
Then replace each number by its rank, where ties are settled by ranking 8i before the square:
a=(3,5,7,9,11,12,14,15,17,..)=A186346
b=(1,2,4,6,8,10,13,16,19,...)=A186347.
|
|
|
MATHEMATICA
|
|
|
|
PROG
|
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
