|
|
A218983
|
|
Power ceiling sequence of sqrt(5).
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
With[{c=Sqrt[5]}, NestList[Ceiling[c #]&, Ceiling[c], 30]] (* Harvey P. Dale, Mar 06 2013 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|