Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Mar 30 2012 17:30:55
%S 1,3,8,21,56,151,410,1114,3027,8227,22362,60785,165230,449141,1220891,
%T 3318725,9021229,24522242,66658364,181196219,492542389,1338869025,
%U 3639423341,9892978333,26891903231,73099771885,198705781579
%N a(0) = 1, then (for n>0) a(n) = floor[(e + 1/e)*a(n-1) - a(n-2)].
%C A recursive series with [a(n+1)/a(n)] converging to e.
%C a(15)/a(14) = 3318725/1220891 = 2.71828115... floor[log a(n)] = n. Example: log a(15) = log 3318725 = 15.01509...; floor(15.015...) = 15.
%e a(5) = 151 = floor[(e + 1/e)*a(4) - a(3)] = floor[(e + 1/e)(56) - 21].
%t a[0] = 1; a[1] = 3; a[n_] := a[n] = Floor[(E + 1/E)*a[n - 1] - a[n - 2]]; Table[ a[n], {n, 0, 27}]
%Y Cf. A085421.
%K nonn
%O 0,2
%A _Gary W. Adamson_, Jul 05 2003
%E More terms from _Robert G. Wilson v_, Jul 13 2003