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

0,1

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

R. Zumkeller, Table of n, a(n) for n = 0..10000

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

Cf. A134451.

Sequence in context: A000035 A188510 A131734 * A327515 A327532 A073445

Adjacent sequences: A134449 A134450 A134451 * A134453 A134454 A134455

Keyword

sign,base

Author

Reinhard Zumkeller, Oct 27 2007

Status

approved