A066661 Numbers m such that floor((1+1/m)^k)=k for an integer k>1.

2, 3, 4, 5, 7, 13, 20, 27, 31, 34, 36, 38, 48, 65, 70, 73, 76, 79, 95, 104, 112, 117, 125, 126, 144, 145, 153, 154, 159, 164, 172, 179, 182, 185, 190, 195, 202, 204, 216, 218, 225, 235, 253, 269, 279, 285, 291, 292, 300, 301, 313, 314, 315, 340, 341, 342, 355, 356, 365

Offset

1,1

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..68896 (terms 1..22681 from David A. Corneth)

David A. Corneth, Identities floor((1+1/a(n)) ^ k) = k corresponding to a(n)

David A. Corneth, PARI program

Vaclav Kotesovec, Plot of a(n)/(n*log(n)) for n = 2..68896

Formula

Conjecture: a(n)=C*n*log(n) asymptotically with C=1.5...

Example

Floor((1+1/4)^11) = 11 hence 4 is in the sequence.

Mathematica

t = Table[Floor[Re[-LambertW[-1, -Log[1 + 1/n]]/Log[1 + 1/n]] + 1], {n, 1, 1000}]; Select[Range[Length[t]], Floor[(1 + 1/#1)^t[[#1]]] == t[[#1]]&] (* Vaclav Kotesovec, Feb 16 2019 *)

Prog

(PARI) See Corneth link \\ David A. Corneth, Feb 15 2019

Crossrefs

Sequence in context: A193769 A226790 A275575 * A268199 A178767 A337188

Adjacent sequences: A066658 A066659 A066660 * A066662 A066663 A066664

Keyword

nonn,easy

Author

Benoit Cloitre, Jan 14 2002

Extensions

Terms 172 and 301 added by Vaclav Kotesovec, Feb 15 2019

Status

approved