A145644 Cubefree part of 10^n.

1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100

Offset

0,2

Comments

Period 3: repeat [1, 10, 100].

Links

Table of n, a(n) for n=0..68.

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

Formula

a(n) = 10^(n mod 3) = A050985(A011557(n)) = A011557(A010872(n)). - Amiram Eldar, Feb 14 2021

From Wesley Ivan Hurt, Apr 18 2021: (Start)

G.f.: (1+10*x+100*x^2)/(1-x^3).

a(n) = a(n-3). (End)

Mathematica

CubefreePart[n_Integer?Positive] := Times @@ Power @@@ ({#[[1]], Mod[ #[[2]], 3]} & /@ FactorInteger[n]); Table[CubefreePart[10^n], {n, 1, 40}]
PadRight[{}, 50, {1, 10, 100}] (* Wesley Ivan Hurt, Apr 18 2021 *)

Prog

(Magma) &cat [[1, 10, 100]^^30]; // Wesley Ivan Hurt, Apr 18 2021

Crossrefs

Cf. A004709, A010872, A011557, A050985, A069705, A145642, A145643.

Sequence in context: A190823 A187019 A292429 * A317055 A284200 A355893

Adjacent sequences: A145641 A145642 A145643 * A145645 A145646 A145647

Keyword

nonn,easy,less

Author

Artur Jasinski, Oct 15 2008

Extensions

Offset corrected by Amiram Eldar, Feb 14 2021

Status

approved