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A290984
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First n-digit number to appear twice in a row in the decimal expansion of e.
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2
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OFFSET
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1,1
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COMMENTS
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18281828 appears in e before any 1-digit, 2-digit, or 3-digit number appears twice in a row.
a(n) starts at positions 31, 49, 97, 2, 112869, 5005575, 1561314, 69682897, ... - Bobby Jacobs, Sep 05 2017
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LINKS
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EXAMPLE
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a(1) = 6 because 6 is the first 1-digit number to appear twice in a row in the decimal expansion of e = 2.718281828459045235360287471352(66)...
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MATHEMATICA
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With[{s = Rest@ First@ RealDigits[N[E, 10^5]]}, Keys@ Merge[#, Identity] &@ Table[TakeSmallest[#, 1] &@ Sort[Map[#[[1, 1]] &, DeleteCases[#, {}]]] &@ Map[SequenceCases[#, {a_, b_} /; b == a + n] &, KeyMap[FromDigits, PositionIndex@ Partition[s, n, 1]]], {n, 4}]] (* Michael De Vlieger, Aug 16 2017 *)
(* or *)
s = First@ RealDigits[E, 10, 51*^5]; Table[p = Partition[s, k, 1]; FromDigits @@ p[[ Select[ Range[ Length@p - k], p[[#]] == p[[#+k]] &, 1]]], {k, 7}] (* much faster, Giovanni Resta, Sep 05 2017 *)
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CROSSREFS
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KEYWORD
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base,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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