A081749 Continued fraction for e/5.

0, 1, 1, 5, 4, 2, 2, 2, 2, 2, 1, 1, 9, 1, 1, 3, 3, 2, 3, 3, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 3, 9, 1, 3, 3, 3, 4, 3, 3, 4, 1, 2, 2, 1, 4, 1, 2, 2, 1, 5, 9, 1, 5, 3, 3, 6, 3, 3, 6, 1, 2, 2, 1, 6, 1, 2, 2, 1, 7, 9, 1, 7, 3, 3, 8, 3, 3, 8, 1, 2, 2, 1, 8, 1, 2, 2, 1, 9, 9, 1, 9, 3, 3, 10, 3, 3, 10, 1, 2, 2, 1, 10, 1, 2

Offset: 1

Author

Benoit Cloitre, Apr 08 2003

Keywords

• nonn
• cofr
• easy

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1).

Crossrefs

Cf. A019762 (decimal expansion).

Cf. A003417 (e), A006083 (e/2), A006084 (e/3), A006085 (e/4).

Programs

Mathematica

ContinuedFraction[E/5, 100] (* Paolo Xausa, Sep 21 2024 *)

PARI

contfrac(exp(1)/5) \\ Michel Marcus, Dec 03 2013

Formula

First 18 terms: 0, 1, 1, 5, 4, 2, 2, 2, 2, 2, 1, 1, 9, 1, 1, 3, 3, 2.

For k >= 1, a(19k)=a(19k+1)=a(19k+16)=a(19k+17)=3; a(19k+2)=a(19k+7)=2k; a(19k+3)=a(19k+6)=a(19k+8)=a(19k+11)=a(19k+14)=1; a(19k+4)=a(19k+5)=a(19k+9)= a(19k+10)=2; a(19k+12)=a(19k+15)=2k+1; a(19k+18)=2k+2.