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A109776
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Self-describing numbers: reading the number gives a (possibly redundant) description of the number.
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4
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22, 4444, 224444, 442244, 444422, 666666, 10123133, 10123331, 10143133, 10143331, 10153133, 10153331, 10163133, 10163331, 10173133, 10173331, 10183133, 10183331, 10193133, 10193331, 10212332, 10213223, 10232132
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OFFSET
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1,1
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COMMENTS
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If abcd... with a, b, c & d integers, then so is cdab... . As an example, since 10123133 is a term so must be 10123331, 10311233, 10313312, 10331231, 10333112, 12103133, 12103331, 12311033, 12313310, 12331031, 12333110, 31101233, 31103312, 31121033, 31123310, 31331012, 31331210, 33101231, 33103112, 33121031, 33123110, 33311012, 33311210.
Therefore 10123133 can be said to be the progenerator or the primitive self-describing number.
Also if we index the number abcd... from left to right, the sum of the odd indexes must equal the number of digits for unique even-indexed digits.
Number of terms < 10^2n: 1, 2, 6, 1043, 5498, ..., .
This sequence is finite with the last term is probably 9998979595959595848484848484848476737373737373736262626262625151515110.
(End)
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LINKS
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EXAMPLE
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"22" does indeed consist of "two 2's".
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MATHEMATICA
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fQ[n_] := Block[{id = IntegerDigits[n]}, If[ OddQ[ Length[id]], Return[False], Union[Reverse@# & /@ Tally[id]] == Union@ Partition[id, 2]]]; k = 1; lst = {}; While[k < 10^7, If[fQ@ k, AppendTo[lst, k]; Print[k]]; k++]; lst (* Robert G. Wilson v, Apr 27 2012 *)
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CROSSREFS
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KEYWORD
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nonn,base,fini
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AUTHOR
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STATUS
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approved
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