login
Least integer k such that Floor(k*f(n+1))>k*f(n), where f(n)=(n^2)/(1+n^2).
1

%I #12 Dec 26 2023 10:16:37

%S 3,6,11,18,27,38,51,66,83,102,123,146,171,198,227,258,291,326,363,402,

%T 443,486,531,578,627,678,731,786,843,902,963,1026,1091,1158,1227,1298,

%U 1371,1446,1523,1602,1683,1766,1851,1938,2027,2118,2211,2306,2403,2502

%N Least integer k such that Floor(k*f(n+1))>k*f(n), where f(n)=(n^2)/(1+n^2).

%C Appears to be essentially the same as A102305, A059100 and A010000. - _R. J. Mathar_, Jun 07 2011

%t Table[k=1; While[Floor[k*((n+1)^2)/(1+(n+1)^2)]<=k*(n^2)/(1+(n^2)), k++]; k, {n,100}]

%Y Cf. A183162.

%K nonn

%O 1,1

%A _Clark Kimberling_, Dec 29 2010