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A134028
Reversal of n in balanced ternary representation.
14
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
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
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.append(x)
l=s[::-1]
return sum(l[i]*3**i for i in range(len(l)))
print([a(n) for n in range(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
KEYWORD
sign,look,base
AUTHOR
Reinhard Zumkeller, Oct 19 2007
STATUS
approved