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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
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
(See A214999.)
With[{c=Sqrt[5]}, NestList[Ceiling[c #]&, Ceiling[c], 30]] (* Harvey P. Dale, Mar 06 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Nov 10 2012
STATUS
approved