A134452 Balanced ternary digital root of n.

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

Author

Reinhard Zumkeller, Oct 27 2007

Keywords

• sign
• base

Comments

a(A005843(n))=0; a(A134453(n))=-1; a(A134454(n))=1; abs(a(A005408(n)))=1;

abs(a(n)) = A000035(n).

Examples

			42 == '+---0' --> +1-1-2-1+0=-2 == '-+' --> -1+1=0;
43 == '+---+' --> +1-1-2-1+1=-1;
		

References

• D. E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, Vol 2, pp 173-175.

Links

• R. Zumkeller, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Digital Root
• Wikipedia, Balanced Ternary

Crossrefs

Cf. A065363, A134453, A134454, A005843, A005408, A000035.

Cf. A134451.

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).