A084798 Least integer such that x^(n+1)/(ceiling(x^n) + a(n)) monotonically decreases to 1, where x=2.30553839092543...

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

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

Table of n, a(n) for n=0..29.

Formula

a(0)=1, a(n+1) = ceiling( x*a(n) + x*ceiling(x^n) - ceiling(x^(n+1)) ), where x=2.30553839092543...

Crossrefs

Sequence in context: A116404 A301600 A084860 * A215149 A017923 A238830

Adjacent sequences: A084795 A084796 A084797 * A084799 A084800 A084801

Keyword

nonn

Author

Paul D. Hanna, Jun 06 2003

Status

approved