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A282171
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Single-digit numbers in the order in which they first appear in the decimal expansion of e, followed by the two-digit numbers in the order in which they appear, then the three-digit numbers, and so on.
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2
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2, 7, 1, 8, 4, 5, 9, 0, 3, 6, 27, 71, 18, 82, 28, 81, 84, 45, 59, 90, 52, 23, 35, 53, 36, 60, 87, 74, 47, 13, 26, 66, 62, 24, 49, 97, 77, 75, 57, 72, 70, 93, 69, 99, 95, 96, 67, 76, 40, 63, 30, 54, 94, 38, 21, 17, 78, 85, 25, 51, 16, 64, 42, 46, 39, 91, 19
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history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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Note that (except for 0 itself), numbers may not begin with 0. So that when we reach ...459045..., this contributes 90 to the sequence but not "04". - N. J. A. Sloane, Feb 08 2017
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LINKS
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EXAMPLE
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Consider the decimal expansion of e=2.718281828459045235360...
The first 4 terms are 2,7,1,8 since these single digits appear in that order above. We do not encounter a different digit till we reach 4,5,9,0, thus these follow the first four in the sequence. We encounter 3 next, and finally 6 and have found all the single digits in the expansion.
a(11)=27 because we find the two-digit group "27" first, followed by a(12)=71, etc. until we exhaust the 90 possible two-digit groups that do not start with a zero.
a(101)=271 because we find the three-digit group "271" first, followed by a(102)=718, etc. until we exhaust the 900 possible 3-digit groups that do not have leading zeros, etc. (End)
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MATHEMATICA
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e = First@ RealDigits@ N[E, 10^6]; MapIndexed[10^(First@ #2 - 1) - 1 - Boole[First@ #2 == 1] + Flatten@ Values@ KeySort@ PositionIndex@ #1 &, Table[SequencePosition[e, IntegerDigits@ k][[1, 1]], {n, 4}, {k, If[n == 1, 0, 10^(n - 1)], 10^n - 1}]] (* Michael De Vlieger, Feb 09 2017, Version 10.1 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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a(5), a(6), a(9), and a(10) inserted by Bobby Jacobs, Feb 09 2017
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STATUS
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approved
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