A219092 a(n) = floor(e^(n + 1/2)).

1, 4, 12, 33, 90, 244, 665, 1808, 4914, 13359, 36315, 98715, 268337, 729416, 1982759, 5389698, 14650719, 39824784, 108254987, 294267566, 799902177, 2174359553, 5910522063, 16066464720, 43673179097, 118716009132, 322703570371

Offset: 0

Author

Clark Kimberling, Jan 01 2013

Keywords

• nonn
• easy

Comments

a(n) is the number k such that {log(k)} < 1/2 < {log(k+1)}, where { } = fractional part. Equivalently, the jump sequence of f(x) = log(x), in the sense that these are the positive integers k for which round(log(k)) < round(log(k+1)). For a guide to related sequences, see A219085.

Examples

			log(1) = 0.000... ; log(2) = 0.693...
log(4) = 1.386... ; log(5) = 1.609...
log(12) = 2.484... ; log(13) = 2.564...
		

Crossrefs

Cf. A001113, A219085.

Programs

Mathematica

Table[Floor[E^(n + 1/2)], {n, 0, 100}]

Formula

a(n) = [e^(n + 1/2)].