A350775 The balanced ternary expansion of a(n) is obtained by multiplying adjacent digits in the balanced ternary expansion of n: a(Sum_{k >= 0} t_k * 3^k) = Sum_{k >= 0} t_k * t_{k+1} * 3^k (with -1 <= t_k <= 1 for any k >= 0).
0, 0, -1, 0, 1, -2, -3, -4, 0, 0, 0, 2, 3, 4, -5, -6, -7, -9, -9, -9, -13, -12, -11, 1, 0, -1, 0, 0, 0, -1, 0, 1, 7, 6, 5, 9, 9, 9, 11, 12, 13, -14, -15, -16, -18, -18, -18, -22, -21, -20, -26, -27, -28, -27, -27, -27, -28, -27, -26, -38, -39, -40, -36, -36
Offset: 0
Examples
The first terms, in decimal and in balanced ternary, are: n a(n) bter(n) bter(a(n)) -- ---- ------- ---------- 0 0 0 0 1 0 1 0 2 -1 1T T 3 0 10 0 4 1 11 1 5 -2 1TT T1 6 -3 1T0 T0 7 -4 1T1 TT 8 0 10T 0 9 0 100 0 10 0 101 0 11 2 11T 1T 12 3 110 10 13 4 111 11
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..9841
Programs
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PARI
a(n) = { my (v=0, p=0, d); for (x=-1, oo, if (n==0, return (v), d=[0, 1, -1][1+n%3]; v+=p*d*3^x; n=(n-d)/3; p=d)) }
Formula
a(n) = 0 iff n belongs to A350776.
Comments