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A134452
Balanced ternary digital root of n.
7
0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0
OFFSET
0,1
COMMENTS
a(A005843(n))=0; a(A134453(n))=-1; a(A134454(n))=1; abs(a(A005408(n)))=1;
abs(a(n)) = A000035(n).
REFERENCES
D. E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, Vol 2, pp 173-175.
LINKS
Eric Weisstein's World of Mathematics, Digital Root
Wikipedia, Balanced Ternary
FORMULA
a(n) = f(n) where f(n) = if n<-1 then f(-A065363(-n)) else (if n>1 then f(A065363(n)) else n).
EXAMPLE
42 == '+---0' --> +1-1-2-1+0=-2 == '-+' --> -1+1=0;
43 == '+---+' --> +1-1-2-1+1=-1;
CROSSREFS
KEYWORD
sign,base,changed
AUTHOR
Reinhard Zumkeller, Oct 27 2007
STATUS
approved