A247778 Least k such that e - (1 + 1/k)^k < 1/n.

1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 34, 35, 36, 38, 39, 40, 42, 43, 44, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 61, 62, 63, 65, 66, 68, 69, 70, 72, 73, 74, 76, 77, 78, 80, 81, 82, 84, 85, 87, 88, 89

Offset: 1

Author

Clark Kimberling, Sep 23 2014

Keywords

• nonn
• easy

Comments

a(n+1) - a(n) is in {1,2} for n >= 1.

Examples

			The values of e - (1 + 1/k)^k for k = 1..8 are approximately 0.718282, 0.468282, 0.347911, 0.276876, 0.229962, 0.196655, 0.171782, 0.152497, so that the first 6 terms of A247778 are 1,2,4,5,6,8.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A247779, A247780.

Programs

Mathematica

z = 600; f[n_] := f[n] = Select[Range[z], E - (1 + 1/#)^# < 1/n &, 1];
u = Flatten[Table[f[n], {n, 1, z}]]       (*A247778*)
d1 = Flatten[Position[Differences[u], 1]] (*A247779*)
d2 = Flatten[Position[Differences[u], 2]] (*A247780*)

PARI

a(n) = {k = 1; while ((exp(1) - (1 + 1/k)^k) >= 1/n, k++); k;} \\ Michel Marcus, Sep 25 2014