A120728 a(n) = floor(e^n) modulo 3.

2, 1, 2, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 2, 2, 1, 0, 2, 2, 2, 1, 1, 1, 2, 2, 0, 2, 1, 2, 0, 2, 1, 1, 2, 2, 2, 1, 0, 1, 2, 0, 2, 1, 0, 0, 0, 2, 1

Offset: 1

Author

Roger L. Bagula, Aug 19 2006

Keywords

• nonn
• less

Comments

This sequence is not unique to e; there are infinitely many numbers x such that mod(floor(x^n), 3) will produce the same sequence. - Franklin T. Adams-Watters, Sep 29 2011

Crossrefs

Cf. A000149.

Programs

Mathematica

Table[Mod[Floor[Exp[n]], 3], {n, 1, 50}]
Table[Floor[Exp[n]] - 3*Floor[Exp[n]/3], {n, 1, 50}]

Formula

a(n) = A000149(n) modulo 3. - Jason Yuen, May 25 2025