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A350657
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a(n) is the greatest value of the orbit of n under repeated application of A350229 (the sum of a number and its balanced ternary digits).
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1
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0, 2, 2, 6, 6, 6, 6, 8, 8, 14, 14, 14, 14, 16, 14, 15, 16, 17, 18, 20, 20, 24, 24, 24, 24, 26, 26, 32, 32, 32, 32, 44, 32, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 45, 46, 47, 48, 50, 50, 51, 52, 53, 54, 56, 56, 60, 60, 60, 60, 62, 62, 68, 68, 68, 68
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OFFSET
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0,2
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COMMENTS
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The sequence { a(n) - n, n >= 0 } has no upper limit (this because the sequence A065363 can be positive on arbitrarily large intervals).
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LINKS
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EXAMPLE
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For n = 9:
- the orbit of 9 contains the following values:
k v bter(v) ds(v)
- -- ------- -----
0 9 100 1
1 10 101 2
2 12 110 2
3 14 1TTT -2
4 12 110 2
- so a(9) = max({ 9, 10, 12, 14 }) = 14.
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MATHEMATICA
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f[n_] := n + Total[If[First@ # == 0, Rest@ #, #] &[Prepend[IntegerDigits[n, 3], 0] //. {x___, y_, k_ /; k > 1, z___} :> {x, y + 1, k - 3, z}]]; Array[Max@ NestWhileList[f, #, UnsameQ, All] &, 67, 0] (* Michael De Vlieger, Jan 15 2022 *)
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PROG
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(PARI) b(n) = my (v=n, d); while (n, n=(n-d=[0, 1, -1][1+n%3])/3; v+=d); v
a(n) = my (s=[]); while (!setsearch(s, n), s=setunion(s, [n]); n=b(n)); s[#s]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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