|
|
A194732
|
|
Units' digits of the nonzero octagonal numbers.
|
|
0
|
|
|
1, 8, 1, 0, 5, 6, 3, 6, 5, 0, 1, 8, 1, 0, 5, 6, 3, 6, 5, 0, 1, 8, 1, 0, 5, 6, 3, 6, 5, 0, 1, 8, 1, 0, 5, 6, 3, 6, 5, 0, 1, 8, 1, 0, 5, 6, 3, 6, 5, 0, 1, 8, 1, 0, 5, 6, 3, 6, 5, 0, 1, 8, 1, 0, 5, 6, 3, 6, 5, 0, 1, 8, 1, 0, 5, 6, 3, 6, 5, 0, 1, 8, 1, 0, 5, 6
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
This is a periodic sequence with period 10 and cycle 1, 8, 1, 0, 5, 6, 3, 6, 5, 0.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = a(n-10).
a(n) = 35 -a(n-1) -a(n-2) -a(n-3) -a(n-4) -a(n-5) -a(n-6) -a(n-7) -a(n-8) -a(n-9).
a(n) = (n*(3*n-2)) mod 10.
G.f.: x*(1 +8*x +x^2 +5*x^4 +6*x^5 +3*x^6 +6*x^7 +5*x^8)/((1-x)*(1+x)*(1 +x +x^2 +x^3 +x^4)*(1 -x +x^2 -x^3 +x^4)).
|
|
EXAMPLE
|
The seventh nonzero octagonal number is A000567(7)=133, which has units' digit 3. Hence a(7)=3.
|
|
MATHEMATICA
|
Table[Mod[n (3 n - 2), 10], {n, 100}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|