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A134028 Reversal of n in balanced ternary representation. 12
0, 1, -2, 1, 4, -11, -2, 7, -8, 1, 10, -5, 4, 13, -38, -11, 16, -29, -2, 25, -20, 7, 34, -35, -8, 19, -26, 1, 28, -17, 10, 37, -32, -5, 22, -23, 4, 31, -14, 13, 40, -119, -38, 43, -92, -11, 70, -65, 16, 97, -110, -29, 52, -83, -2, 79, -56, 25, 106, -101, -20, 61, -74, 7, 88, -47, 34, 115, -116, -35, 46, -89, -8, 73, -62, 19, 100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

As the graph demonstrates, the sequence makes large negative steps at terms (3^i+1)/2. These steps divide the graph into conspicuous blocks. - N. J. A. Sloane, Jul 03 2016

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, Reversal

Wikipedia, Balanced Ternary

FORMULA

a(A134027(n)) = A134027(n);

A134021(ABS(a(n))) <= A134021(n).

EXAMPLE

20 = 1*3^3 - 1*3^2 + 1*3^1 - 1*3^0 == '+-+-'

=> a(20) = -1*3^3 + 1*3^2 - 1*3^1 + 1*3^0 = -20;

21 = 1*3^3 - 1*3^2 + 1*3^1 + 0*3^0 == '+-+0'

=> a(21) = 0*3^3 + 1*3^2 - 1*3^1 + 1*3^0 = 7;

22 = 1*3^3 - 1*3^2 + 1*3^1 + 1*3^0 == '+-++'

=> a(22) = 1*3^3 + 1*3^2 - 1*3^1 + 1*3^0 = 34;

23 = 1*3^3 + 0*3^2 - 1*3^1 - 1*3^0 == '+0--'

=> a(23) = -1*3^3 - 1*3^2 + 0*3^1 + 1*3^0 = -35;

24 = 1*3^3 + 0*3^2 - 1*3^1 + 0*3^0 == '+0-0'

=> a(24) = 0*3^3 - 1*3^2 + 0*3^1 + 1*3^0 = -8;

25 = 1*3^3 + 0*3^2 - 1*3^1 + 1*3^0 == '+0-+'

=> a(25) = 1*3^3 - 1*3^2 + 0*3^1 + 1*3^0 = 19.

PROG

(Python)

def a(n):

    if n==0: return 0

    s=[]

    x=0

    while n>0:

        x=n%3

        n=n/3

        if x==2:

            x=-1

            n+=1

        s+=[x, ]

    l=s[::-1]

    t=0

    for i in xrange(len(l)): t+=l[i]*3**i

    return t

print [a(n) for n in xrange(101)] # Indranil Ghosh, Jun 10 2017

CROSSREFS

Cf. A117966 (balanced ternary representation), A030102, A134021, A274107.

A134027 gives the numbers whose balanced ternary representation is palindromic.

Sequence in context: A121198 A234599 A016544 * A111479 A323937 A088137

Adjacent sequences:  A134025 A134026 A134027 * A134029 A134030 A134031

KEYWORD

sign,look,base

AUTHOR

Reinhard Zumkeller, Oct 19 2007

STATUS

approved

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Last modified April 23 18:15 EDT 2019. Contains 322387 sequences. (Running on oeis4.)