A114956 - OEIS

%I #20 Sep 10 2024 08:45:07

%S 1,1,2,3,4,6,7,9,10,11,12,13,14,15,15,16,16,16,16,16,16,16,16,16,16,

%T 16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,

%U 16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16

%N a(n) = ceiling(a(n-1)^(3/4) + a(n-2)^(3/4)), with a(0) = a(1) = 1.

%C a(17) = 16 is exactly 16^(3/4) + 16^(3/4) = 16. This is a fixed point, so a(n) = 16 for all n>14.

%e a(2) = ceiling(a(0)^(3/4) + a(1)^(3/4)) = ceiling(1^(3/4) + 1^(3/4)) = 2.

%e a(3) = ceiling(a(1)^(3/4) + a(2)^(3/4)) = ceiling(1^(3/4) + 2^(3/4)) = ceiling(2.68179283) = 3.

%e a(4) = ceiling(2^(3/4) + 3^(3/4)) = ceiling(3.96129989) = 4.

%e a(5) = ceiling(3^(3/4) + 4^(3/4)) = ceiling(5.10793418) = 6.

%e a(6) = ceiling(4^(3/4) + 6^(3/4)) = ceiling(6.66208575) = 7.

%t RecurrenceTable[{a[0]==1,a[1]==1,a[n]==Ceiling[a[n-1]^(3/4)+ a[n-2]^(3/4)]}, a[n],{n,80}] (* _Harvey P. Dale_, Jul 22 2011 *)

%Y Cf. A000283, A112961, A112969, A114793.

%K easy,nonn

%O 0,3

%A _Jonathan Vos Post_, Feb 21 2006

%E Edited by _N. J. A. Sloane_, May 20 2006