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 A109776 Self-describing numbers: reading the number gives a (possibly redundant) description of the number. 4
 22, 4444, 224444, 442244, 444422, 666666, 10123133, 10123331, 10143133, 10143331, 10153133, 10153331, 10163133, 10163331, 10173133, 10173331, 10183133, 10183331, 10193133, 10193331, 10212332, 10213223, 10232132 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Robert G. Wilson v, May 05 2012: (Start) If abcd… with a, b, c & d integers, then so is cdab… . As an example, since 10123133 is a member 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) LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..10538 The Prime Puzzles & Problems Connection by Carlos Rivera, Puzzle"> 324. Self-descriptive numbers EXAMPLE "22" does indeed consist of "two 2's". MATHEMATICA 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 *) CROSSREFS Cf. A108810, A173101, A005150. Sequence in context: A114942 A155885 A218719 * A110802 A200460 A202054 Adjacent sequences:  A109773 A109774 A109775 * A109777 A109778 A109779 KEYWORD nonn,base,fini AUTHOR Jud McCranie, Aug 15 2005 STATUS approved

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Last modified October 22 14:53 EDT 2018. Contains 316490 sequences. (Running on oeis4.)