A343602 For any positive number n, the balanced ternary representation of a(n) is obtained by left-rotating the balanced ternary representation of n until a nonzero digit appears again as the leftmost digit; a(0) = 0.
0, 1, -2, 3, 4, -11, -8, -5, -6, 9, 12, 7, 10, 13, -38, -35, -32, -29, -26, -23, -20, -17, -14, -33, -24, -15, -18, 27, 36, 21, 30, 39, 16, 19, 22, 25, 28, 31, 34, 37, 40, -119, -116, -113, -110, -107, -104, -101, -98, -95, -92, -89, -86, -83, -80, -77, -74
Offset: 0
Examples
The first terms, in base 10 and in balanced ternary (where T denotes the digit -1), are: n a(n) bter(n) bter(a(n)) -- ---- ------- ---------- 0 0 0 0 1 1 1 1 2 -2 1T T1 3 3 10 10 4 4 11 11 5 -11 1TT TT1 6 -8 1T0 T01 7 -5 1T1 T11 8 -6 10T T10 9 9 100 100 10 12 101 110 11 7 11T 1T1 12 10 110 101 13 13 111 111 14 -38 1TTT TTT1 15 -35 1TT0 TT01
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..9841
Crossrefs
Programs
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PARI
a(n) = { my (d = [], t); while (n, d = concat(t = centerlift(Mod(n,3)), d); n = (n-t)\3); for (k=2, #d, if (d[k], return (fromdigits(concat(d[k..#d], d[1..k-1]), 3)))); return (fromdigits(d, 3)) }
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