|
|
A084798
|
|
Least integer such that x^(n+1)/(ceiling(x^n) + a(n)) monotonically decreases to 1, where x=2.30553839092543...
|
|
1
|
|
|
1, 2, 6, 15, 36, 84, 195, 451, 1041, 2402, 5539, 12772, 29447, 67893, 156531, 360889, 832045, 1918313, 4422746, 10196812, 23509143, 54201233, 124963024, 288107051, 664241868, 1531435129, 3530782484, 8140354569, 18767899975, 43270113911
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
x=2.30553839092543... is the unique value at which the limit is 1: lim_{n->infinity} x^(n+1)/(ceiling(x^n) + a(n)) = 1; a(n) ~ (x-1)*x^n.
|
|
LINKS
|
|
|
FORMULA
|
a(0)=1, a(n+1) = ceiling( x*a(n) + x*ceiling(x^n) - ceiling(x^(n+1)) ), where x=2.30553839092543...
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|