A343603 For any positive number n, the balanced ternary representation of a(n) is obtained by right-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, -7, -8, 11, -6, 9, 12, -5, 10, 13, -22, -25, 32, -21, -26, 33, -20, 29, 34, -19, -24, 35, -18, 27, 36, -17, 30, 37, -16, -23, 38, -15, 28, 39, -14, 31, 40, -67, -76, 95, -66, -79, 96, -65, 86, 97, -64, -75, 98, -63, -80, 99, -62, 87, 100, -61
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 -7 1TT T1T 6 -8 1T0 T01 7 11 1T1 11T 8 -6 10T T10 9 9 100 100 10 12 101 110 11 -5 11T T11 12 10 110 101 13 13 111 111 14 -22 1TTT T1TT 15 -25 1TT0 T01T
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); forstep (k=#d, 1, -1, if (d[k], return (fromdigits(concat(d[k..#d], d[1..k-1]), 3)))); return (fromdigits(d, 3)) }
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