A247784 a(n) = floor(1/(e - (1 + 1/n)^n)).

1, 2, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9, 10, 10, 11, 12, 13, 13, 14, 15, 16, 16, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 24, 25, 26, 27, 27, 28, 29, 30, 30, 31, 32, 33, 33, 34, 35, 35, 36, 37, 38, 38, 39, 40, 41, 41, 42, 43, 44, 44, 45, 46, 47, 47, 48, 49, 49, 50

Offset: 1

Author

Clark Kimberling, Sep 24 2014

Keywords

• nonn
• easy

Comments

a(n+1) - a(n) is in {0,1} for n >= 0.

Links

• Clark Kimberling, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A247778, A247785, A247786.

Programs

Magma

[Floor(1/(Exp(1) - (1 + 1/n)^n)): n in [1..100]]; // G. C. Greubel, Sep 14 2018

Mathematica

z = 200; t = Table[Floor[1/(E - (1 + 1/k)^k)], {k, 1, z}]   (*A247784*)
d = Differences[t]
Flatten[Position[d, 0]]  (*A247785*)
Flatten[Position[d, 1]]  (*A247786*)

PARI

a(n) = floor(1/(exp(1) - (1 + 1/n)^n)); \\ Michel Marcus, Sep 26 2014

Formula

a(n) ~ 2*exp(-1) * n. - Vaclav Kotesovec, Oct 09 2014