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A325479
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Decimal expansion of a normal number in base 10, which, on average, up to any given integer appearance (above 11), is more compact than Champernowne's constant, and more compact than A189823.
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1
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1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 2, 0, 2, 1, 2, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 3, 0, 3, 2, 3, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 4, 0, 4, 3, 4, 4, 6, 4, 7, 4, 8, 4, 9, 5, 0, 5, 4, 5, 5, 7, 5, 8, 5, 9, 6, 0, 6, 5, 6, 6, 8, 6, 9, 7, 0, 7, 6, 7, 7, 9, 8, 0, 8, 7, 8, 8, 9, 0, 9, 9, 1, 0, 0, 1, 0, 2, 1, 0, 3, 1, 0, 4, 1, 0, 5, 1, 0, 6, 1, 0, 7, 1
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OFFSET
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0,2
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COMMENTS
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This number is normal in base 10. On average, any integer above 11 can be found in this decimal expansion at a place earlier than in Champernowne's constant, thus making it a more densely encoded normal number.
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LINKS
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EXAMPLE
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0.1234567891011314151617181920212242526272829303132335363738394...
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MATHEMATICA
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isitthere[seq_, n_] := SequencePosition[seq, IntegerDigits[n]]; addtoseq[seq_, n_] := Module[{}, id = IntegerDigits[n]; len = Length[id]; For[i = 1, i < len, i++, If[seq[[i - len;; ]] == id[[;; -i - 1]], Return[Join[seq, id[[-i;; ]]]]]]; Return[ Join[seq, id]]]; generate[upto_] := Module[{}, start = {1}; For[m = 1, m <= upto, m++, If[isitthere[start, m] === {}, start = addtoseq[start, m]]]; start]
(* To generate terms which include all positive integers up to 200: *)
generate[200]
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CROSSREFS
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Cf. A033307 (Champernowne's constant), A189823 (reduced Champernowne constant).
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KEYWORD
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AUTHOR
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STATUS
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approved
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