|
|
A001903
|
|
Final digit of 7^n.
|
|
5
|
|
|
1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Period 4: repeat [1, 7, 9, 3]. - Joerg Arndt, Aug 12 2014
|
|
LINKS
|
Edward Omey and Stefan Van Gulck, What are the last digits of ...?, International Journal of Mathematical Education in Science and Technology, (2015) 46:1, 147-155.
|
|
FORMULA
|
a(n) = a(n-1) - a(n-2) + a(n-3) for n > 2.
G.f.: ( 1+6*x+3*x^2 ) / ( (1-x)*(1+x^2) ). (End)
a(n) = 5 - (2-i)*(-i)^n - (2+i)*i^n, where i=sqrt(-1).
|
|
MAPLE
|
|
|
MATHEMATICA
|
|
|
PROG
|
(Sage) [power_mod(7, n, 10)for n in range(0, 81)] # Zerinvary Lajos, Nov 03 2009
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|