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A304274
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The concatenation of the first n elements is the largest positive even number with n digits when written in base 3/2.
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3
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2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2
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OFFSET
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1,1
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COMMENTS
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This sequence is possible due to the fact that the largest even integers are prefixes of each other.
A304272(n) is the largest even integer with n digits.
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LINKS
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FORMULA
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Sum_{i=0..n-1} (3/2)^i*a(n-i) = A305497(n). (End)
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EXAMPLE
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Number 8 in base 3/2 is 212, and it is the largest even integer with 3 digits in base 3/2. Its prefix 21 is 4: the largest even integer with 2 digits in base 3/2.
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MAPLE
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b:= proc(n) option remember; `if`(n=1, 2,
(t-> t+irem(t, 2))(b(n-1)*3/2))
end:
a:= n-> b(n+1)-3/2*b(n)+1:
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MATHEMATICA
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b[n_] := b[n] = If[n == 1, 2, Function[t, t + Mod[t, 2]][3/2 b[n-1]]];
a[n_] := b[n+1] - 3/2 b[n] + 1;
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CROSSREFS
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Cf. A005428, A070885, A073941, A081848, A024629, A246435, A304024, A304025, A303500, A304272, A304273, A305497, A305498.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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