A105397 Periodic with period 2: repeat [4,2].

4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2

Offset: 0

Author

Eric Angelini, May 01 2005

Keywords

• easy
• nonn

Comments

A simple "Fractal Jump Sequence" (FJS). An FJS is a sequence of digits containing an infinite number of copies of itself. Modus operandi: underline the first digit "a" of such a sequence then jump over the next "a" digits and underline the digit "b" on which you land. Jump from there over the next "b" digits and underline the digit "c" on which you land. Etc. The "abc...n..." succession of underlined digits is the sequence itself.

Simple continued fraction of 2+sqrt(6). - R. J. Mathar, Nov 21 2011

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1).

Crossrefs

Cf. A010694 (period 2, repeat [2,4]).

First differences of A007310. - Fred Daniel Kline, Aug 17 2020

Programs

Maple

A105397:=n->3 + (-1)^n; seq(A105397(n), n=0..100); # Wesley Ivan Hurt, Mar 14 2014

Mathematica

Table[3 + (-1)^n, {n, 0, 100}] (* Wesley Ivan Hurt, Mar 14 2014 *)
LinearRecurrence[{0, 1},{4, 2},75] (* Ray Chandler, Aug 25 2015 *)

PARI

contfrac(2+sqrt(6)) \\ Michel Marcus, Mar 18 2014

Formula

a(n) = 3 + (-1)^n = 4 - 2*(n mod 2) = 2 * 2^((n+1) mod 2). - Wesley Ivan Hurt, Mar 14 2014

Extensions

Edited by N. J. A. Sloane, Jun 08 2010