A085560 a(0) = 1, then (for n>0) a(n) = floor[(e + 1/e)*a(n-1) - a(n-2)].

1, 3, 8, 21, 56, 151, 410, 1114, 3027, 8227, 22362, 60785, 165230, 449141, 1220891, 3318725, 9021229, 24522242, 66658364, 181196219, 492542389, 1338869025, 3639423341, 9892978333, 26891903231, 73099771885, 198705781579

Offset: 0

Author

Gary W. Adamson, Jul 05 2003

Keywords

• nonn

Comments

A recursive series with [a(n+1)/a(n)] converging to e.

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.

Examples

			a(5) = 151 = floor[(e + 1/e)*a(4) - a(3)] = floor[(e + 1/e)(56) - 21].
		

Crossrefs

Cf. A085421.

Programs

Mathematica

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}]

Extensions

More terms from Robert G. Wilson v, Jul 13 2003