A105397 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

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) = A176213. - R. J. Mathar, Nov 21 2011

Decimal expansion of 14/33. - Elmo R. Oliveira, Sep 26 2025

REFERENCES

Harold Davenport, The Higher Arithmetic, Cambridge University Press, 8th ed., 2008, p. 86.

LINKS

Table of n, a(n) for n=0..101.

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

FORMULA

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

From Elmo R. Oliveira, Sep 26 2025: (Start)

G.f.: 2*(2 + x)/(1 - x^2).

E.g.f.: 4*cosh(x) + 2*sinh(x).