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 A108551 Self-descriptive numbers in various bases represented in base 10. 2
 100, 136, 1425, 389305, 8946176, 225331713, 6210001000, 186492227801, 6073061476032, 213404945384449, 8054585122464440, 325144322753909625, 13983676842985394176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. REFERENCES Clifford Pickover, Keys to Infinity, Chapter 28, "Chaos in Ontario." New York: Wiley, pp. 217-219, 1995. LINKS Eric Weisstein's World of Mathematics, Self-Descriptive Number. Wikipedia, The Free-Content Encyclopedia, Self Descriptive Numbers EXAMPLE 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. MATHEMATICA 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}] (* Robert G. Wilson v, Jun 07 2005 *) CROSSREFS Cf. A046043. See A274943 for another version. Sequence in context: A127336 A045211 A244391 * A096598 A070760 A161902 Adjacent sequences:  A108548 A108549 A108550 * A108552 A108553 A108554 KEYWORD base,nonn,more AUTHOR Alonso del Arte, Jun 07 2005 STATUS approved

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