A079663 Sequence of the radicands that give the best radical approach to e.

1, 2, 3, 6, 7, 19, 20, 148, 403, 1096, 1097, 2980, 2981, 8103, 59874, 162755, 1202603, 1202604, 3269017, 8886110, 8886111, 24154952, 24154953, 65659969, 178482301, 3584912846, 9744803446, 26489122130, 72004899337, 195729609428

Offset: 1

Author

Carlos Alves, Jan 24 2003

Keywords

• nonn

Comments

Numbers n such that n^(1/m) is closer to e than for previous n. m is given by the Floor/Ceiling of Log[n].

Each group of entries exceed the previous group by e^k where k is an integer.

Examples

			e-1^1 > e-2^1 > 3^1-e > e-6^(1/2) > e-7^(1/2) > e-19^(1/3) > e-20^(1/3) > ...
		

Crossrefs

Cf. A004791, A080021.

Programs

Mathematica

ls = {}; mx = 1; Do[mn = Min[Abs[{n^(1/Floor[Log[n]]) - E, E - n^(1/Ceiling[Log[n]])}]]; If[mn < mx, mx = mn; AppendTo[ls, {n, mx}]], {n, 3, 500000}]; N[ls] // TableForm

Extensions

Edited and extended by Robert G. Wilson v, Jan 24 2003