|
|
A267317
|
|
a(n) = final digit of 2^n-1.
|
|
1
|
|
|
0, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5, 1, 3, 7, 5
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Decimal expansion of 25/1818.
Period 4: repeat [1, 3, 7, 5] for n > 0.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x*(1 + 2*x + 5*x^2)/(1 - x + x^2 - x^3).
a(n) = (1+(-1)^n)*(-1)^(n*(n-1)/2)/2 + 3*(1-(-1)^n)*(-1)^(n*(n+1)/2)/2 + 4 for n > 0, a(0) = 0. [Bruno Berselli, Jan 13 2016]
a(n) = a(n-4) for n>4.
a(n) = a(n-1) - a(n-2) + a(n-3) for n > 3.
a(n) = 4 + cos(n*Pi/2) - 3*sin(n*Pi/2) for n > 0. (End)
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[Mod[2^n - 1, 10], {n, 0, 120}]
|
|
PROG
|
(Magma) [0] cat &cat[[1, 3, 7, 5]^^25]; // Bruno Berselli, Jan 13 2016
(PARI) a(n) = if(n==0, 0, if(n%4==0, 5, if(n%4==1, 1, if(n%4==2, 3, if(n%4==3, 7))))) \\ Felix Fröhlich, Jan 19 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|