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A304273
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The concatenation of the first n terms is the smallest positive even number with n digits when written in base 3/2 (cf. A024629).
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4
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2, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0
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OFFSET
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1,1
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COMMENTS
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This sequence exists since the smallest even integers (see A303500) are prefixes of each other.
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LINKS
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FORMULA
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EXAMPLE
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The number 5 in base 3/2 is 22, and the number 6 is 210. Therefore 210 is the smallest even integer with 3 digits in base 3/2. Its prefix 21 is 4: the smallest 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<2, 2*n,
(t-> t+irem(t, 2))(b(n-1)*3/2))
end:
a:= n-> b(n)-3/2*b(n-1):
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MATHEMATICA
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b[n_] := b[n] = If[n < 2, 2*n, Function[t, t + Mod[t, 2]][3/2 b[n - 1]]]; a[n_] := b[n] - 3/2 b[n - 1]; Table[a[n], {n, 1, 105}] (* Robert P. P. McKone, Feb 12 2021 *)
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CROSSREFS
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Cf. A005428, A070885, A073941, A081848, A024629, A246435, A304024, A304025, A303500, A304272, A304274.
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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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