|
|
A073359
|
|
Nested floor product of n and fractions (2k+2)/(2k+1) for all k>=0, divided by 2.
|
|
7
|
|
|
1, 3, 6, 9, 13, 19, 24, 31, 39, 45, 54, 66, 73, 90, 103, 111, 126, 144, 153, 174, 193, 199, 229, 240, 264, 283, 306, 324, 354, 381, 403, 421, 463, 474, 504, 546, 555, 594, 630, 660, 679, 735, 741, 789, 846, 859, 903, 949, 966, 1011
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
By definition, a(n)=(1/2)[...[[[[n(2/1)](4/3)](6/5)]...(2k+2)/(2k+1)]..., where [x] = floor of x; this infinite nested floor product will eventually level-off at a(n).
|
|
EXAMPLE
|
a(3) = 6 since (1/2)[[[[[[3(2/1)](4/3)](6/5)](8/7)](10/9)](12/11)] = (1/2)[[[[[6(4/3)](6/5)](8/7)](10/9)](12/11)] = (1/2)[[[[8(6/5)](8/7)](10/9)](12/11)] = (1/2)[[[9(8/7)](10/9)](12/11)] = (1/2)[[10(10/9)](12/11)] = (1/2)[11(12/11)] = 6. [Minor correction by M. F. Hasler, Nov 23 2016]
|
|
PROG
|
(PARI) apply( A073359(n)=forstep(k=2, 9e9, 2, n==(n=floor(n*k/(k-1)))&&return(n\2)), [1..100]) \\ M. F. Hasler, Nov 23 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|