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

0,1

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...

Links

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

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A214992, A214999, A215091, A218982.

Sequence in context: A081037 A019489 A077852 * A020746 A033303 A078056

Adjacent sequences: A218980 A218981 A218982 * A218984 A218985 A218986

Keyword

nonn,easy

Author

Clark Kimberling, Nov 10 2012

Status

approved