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A047841
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Autobiographical numbers: Fixed under operator T (A047842): "Say what you see".
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24
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22, 10213223, 10311233, 10313314, 10313315, 10313316, 10313317, 10313318, 10313319, 21322314, 21322315, 21322316, 21322317, 21322318, 21322319, 31123314, 31123315, 31123316, 31123317, 31123318, 31123319
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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A digit count numerically summarizes the frequency of digits 0 through 9 in that order when they occur in a number.
This uses a different method from A108810. Here the digits are described in increasing order, whereas in A108810 they can be described in any order.
This sequence is finite, since T(x) < x for every x with at least 22 digits. Last term is a(109) = 101112213141516171819. - Schimke
A character in the Verghese (2009) novel declares that 10213223 "is the only number that describes itself when you read it." - Alonso del Arte, Jan 26 2014
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REFERENCES
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J. N. Kapur, Reflections of a Mathematician, Chapter 33, pp. 314-318, Arya Book Depot, New Delhi 1996.
Abraham Verghese, Cutting for Stone: A Novel. New York: Alfred A. Knopf (2009): 294.
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LINKS
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EXAMPLE
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10313314 contains 1 0's, 3 1's, 3 3's and 1 4's, hence T(10313314) = 10313314 is in the sequence
The entry 3122331418, for instance, is a member since it is indeed made up of three 1's, two 2's, three 3's, one 4 and one 8.
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CROSSREFS
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Cf. A005151, which is the sequence 1, T(1), T(T(1)), .. ending in the fixed-point 21322314.
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KEYWORD
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nonn,fini,full,base,nice,eigen
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AUTHOR
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Ulrich Schimke (ulrschimke(AT)aol.com)
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EXTENSIONS
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STATUS
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approved
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