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A108551 Self-descriptive numbers in various bases represented in base 10. 1
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

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

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}] (from Robert G. Wilson v, Jun 07 2005)

CROSSREFS

Cf. A046043.

Sequence in context: A127336 A045211 A244391 * A096598 A070760 A161902

Adjacent sequences:  A108548 A108549 A108550 * A108552 A108553 A108554

KEYWORD

base,nonn

AUTHOR

Alonso del Arte, Jun 07 2005

STATUS

approved

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Last modified July 26 15:24 EDT 2014. Contains 244952 sequences.