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A057846
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Sort the digits of n into alphabetical order (the "Obsessive Filer's Sequence").
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6
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 41, 51, 16, 17, 81, 91, 20, 12, 22, 32, 42, 52, 62, 72, 82, 92, 30, 13, 32, 33, 43, 53, 63, 73, 83, 93, 40, 41, 42, 43, 44, 54, 46, 47, 84, 49, 50, 51, 52, 53, 54, 55, 56, 57, 85, 59, 60, 16, 62, 63, 46, 56, 66, 76, 86, 96, 70, 17, 72, 73, 47, 57, 76, 77, 87
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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The digits of each number n (written in base 10) are put into alphabetical order by their English name. This means a given term's digits must be in this order: 8, 5, 4, 9, 1, 7, 6, 3, 2, 0. It's easy to see that any n-digit term (with digits in this order) with distinct digits, none zero, occurs exactly n! times in the sequence.
Since 0 = "zero" is sorted last, this works well for the English language. But the same cannot be "coded without loss" on OEIS for languages where the name for 0 is not sorted last: E.g., in German, 0="null" comes before, e.g., 2="zwei", which would yield "02" for 20, but leading zeros are not allowed on the OEIS. - M. F. Hasler, Jul 28 2013
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REFERENCES
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M. J. Halm, Sequences (Re)discovered, Mpossibilities 81 (Aug. 2002), p. 1.
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LINKS
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EXAMPLE
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a(14)=41 because the digits of 14, 1 (one) and 4 (four), are in alphabetical order when arranged as 4, then 1, so 41.
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MATHEMATICA
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s = {9, 4, 8, 7, 2, 1, 6, 5, 0, 3}; Table[FromDigits[Sort[IntegerDigits[n], s[[#1 + 1]] < s[[#2 + 1]] &]], {n, 78}] (* Ivan Neretin, Jul 09 2015 *)
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PROG
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(PARI) A057846(n, o=[9, 4, 8, 7, 2, 1, 6, 5, 0, 3])= {sum(i=1, #n=vecsort(digits(n), (a, b)->o[b+1]-o[a+1]), n[i]*10^i)/10} \\ - M. F. Hasler, Jul 28 2013
(Python)
def k(c): return "8549176320".index(c)
def a(n): return int("".join(sorted(str(n), key=k)))
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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