A218983 Power ceiling sequence of sqrt(5).

3, 7, 16, 36, 81, 182, 407, 911, 2038, 4558, 10192, 22791, 50963, 113957, 254816, 569786, 1274081, 2848932, 6370406, 14244661, 31852031, 71223307, 159260157, 356116538, 796300787, 1780582691, 3981503937, 8902913456

Offset: 0

Author

Clark Kimberling, Nov 10 2012

Keywords

• nonn
• easy

Comments

See A214992 for a discussion of power ceiling sequence and the power ceiling function, p4(x) = limit of a(n,x)/x^n. The present sequence is a(n,r), where r = sqrt(5), and the limit p4(r) = 3.2616480254413398807499379112702935254866963...

See A214999 for the power floor function, p1(x). For comparison of p4 and p1, limit(p4(r)/p1(r)) = 2.183820340393031136325385184014007307594650...

Examples

			a(0) = ceiling(r) = 3, where r = sqrt(5);
a(1) = ceiling(3*r) = 7; a(2) = ceiling(7*r ) = 16.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A214992, A214999, A215091, A218982.

Programs

Mathematica

(See A214999.)
With[{c=Sqrt[5]},NestList[Ceiling[c #]&,Ceiling[c],30]] (* Harvey P. Dale, Mar 06 2013 *)

Formula

a(n) = ceiling(x*a(n-1)), where x=sqrt(5), a(0) = ceiling(x).