A095394 a(n) = Floor[n^((n)/(n+1))], integer part of n^x where x = n/(n+1) < 1.

1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 61, 62, 63, 64, 65, 66, 67, 68

Offset: 1

Author

Labos Elemer, Jun 17 2004

Keywords

• nonn

Comments

1, 3, 9, 24, 61, 160, 420, 1120, ... appear in the sequence twice. The ratio of such numbers converges to e. [Charles R Greathouse IV, Oct 26 2011]

Crossrefs

Cf. A059921.

Programs

Mathematica

Table[Floor[N[x^((x+1)/(x)), 50]], {x, 1, 15}]

PARI

a(n)=floor(n^(n/(n+1.))) \\ Charles R Greathouse IV, Oct 26 2011