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A352501
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a(n) is the distance from n to the nearest integer that can be added to n without carries in balanced ternary.
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1
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0, 1, 1, 2, 1, 1, 2, 4, 4, 5, 4, 4, 2, 1, 1, 2, 4, 4, 5, 7, 10, 11, 13, 10, 11, 13, 13, 14, 13, 13, 11, 10, 13, 11, 10, 7, 5, 4, 4, 2, 1, 1, 2, 4, 4, 5, 7, 10, 11, 13, 10, 11, 13, 13, 14, 16, 19, 20, 22, 28, 29, 31, 31, 32, 34, 37, 38, 40, 28, 29, 31, 31, 32
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OFFSET
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0,4
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COMMENTS
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Two integers can be added without carries in balanced ternary if they have no equal nonzero digit at the same position.
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LINKS
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Rémy Sigrist, Table of n, a(n) for n = 0..9841
Wikipedia, Balanced ternary
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FORMULA
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a(n) = 1 iff n > 0 and n belongs to A003462 or A007051.
a(3*n) = 3*a(n)+1 for any n > 0.
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EXAMPLE
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For n = 7:
- the numbers k around 7, alongside their distance to 7, balanced ternary expansion and whether they require carries when added to 7, are:
k d bter(k) carries?
-- - ------- --------
3 4 10 no
4 3 11 yes
5 2 1TT yes
6 1 1T0 yes
7 0 1T1 yes
8 1 10T yes
9 2 100 yes
10 3 101 yes
11 4 11T yes
- so a(7) = 4.
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PROG
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(PARI) ok(u, v) = { while (u && v, my (uu=[0, +1, -1][1+u%3], vv=[0, +1, -1][1+v%3]); if (abs(uu+vv)>1, return (0)); u=(u-uu)/3; v=(v-vv)/3); return (1) }
a(n) = for (d=0, oo, if (ok(n, n-d) || ok(n, n+d), return (d)))
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CROSSREFS
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Cf. A003462, A007051, A059095, A353158.
Sequence in context: A108746 A333270 A333272 * A119558 A333450 A210112
Adjacent sequences: A352498 A352499 A352500 * A352502 A352503 A352504
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KEYWORD
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nonn,base
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AUTHOR
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Rémy Sigrist, Apr 28 2022
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STATUS
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approved
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