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A108551
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Self-descriptive numbers in various bases represented in base 10.
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0
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100, 136, 1425, 389305, 8946176, 225331713, 6210001000, 186492227801, 6073061476032, 213404945384449, 8054585122464440, 325144322753909625, 13983676842985394176
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OFFSET
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1,1
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COMMENTS
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A self-descriptive number in base b has b digits, indexed by 0 ... b-1 and for all n, the n-th digit equals the number of n's in the number. In base 10 there is exactly one such number, 6210001000.
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REFERENCES
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Clifford Pickover, Keys to Infinity, Chapter 28, "Chaos in Ontario." New York: Wiley, pp. 217-219, 1995.
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LINKS
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Table of n, a(n) for n=1..13.
Eric Weisstein's World of Mathematics, Self-Descriptive Number.
Wikipedia, The Free-Content Encyclopedia, Self Descriptive Numbers
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EXAMPLE
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1210_4 = 100, 2020_4 = 136, 21200_5 = 1425, 3211000_7 = 389305,
42101000_8 = 8946176, 521001000_9 = 225331713, 6210001000_10,
72100001000_11 = 186492227801, 821000001000_12 = 6073061476032,
9210000001000_13 = 213404945384449, (10)2100000001000_14 =
8054585122464440, (11)21000000001000_15 = 325144322753909625,
(12)21000000001000_16 = 13983676842985394176, etc.
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MATHEMATICA
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Do[id = IntegerDigits[n, base]; If[id == (Count[id, # ] & /@ Range[0, base - 1]), Print[n]], {base, 2, 10}, {n, base^(base - 1), (base^base) - 1, base}]
(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) fQ[lst_] := (lst == (Count[lst, # ] & /@ Range[0, Length[lst] - 1])); f[n_] := Block[{pts = PadLeft[ #, n] & /@ Partitions[n], k = 1, l = PartitionsP[n], lst = {}}, While[k < l, AppendTo[ lst, FromDigits[ Flatten[ Select[ Permutations[ pts[[k]]], fQ[ # ] &]], n]]; k++ ]; Drop[ Union[ lst], 1]]; Table[ f[n], {n, 2, 15}] (from Robert G. Wilson v, Jun 07 2005)
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CROSSREFS
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Cf. A046043.
Sequence in context: A109881 A127336 A045211 * A096598 A070760 A161902
Adjacent sequences: A108548 A108549 A108550 * A108552 A108553 A108554
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KEYWORD
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base,nonn
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AUTHOR
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Alonso del Arte, Jun 07 2005
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STATUS
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approved
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