

A108551


Selfdescriptive numbers in various bases represented in base 10.


1



100, 136, 1425, 389305, 8946176, 225331713, 6210001000, 186492227801, 6073061476032, 213404945384449, 8054585122464440, 325144322753909625, 13983676842985394176
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OFFSET

1,1


COMMENTS

A selfdescriptive number in base b has b digits, indexed by 0 ... b1 and for all n, the nth 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. 217219, 1995.


LINKS

Table of n, a(n) for n=1..13.
Eric Weisstein's World of Mathematics, SelfDescriptive Number.
Wikipedia, The FreeContent 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



