A173101 -id:A173101 - cp's OEIS frontend

A108810 Self-describing primes.

10153331, 10173133, 10233221, 10311533, 10322321, 12103331, 12163133, 12163331, 12193133, 12311933, 12313319, 15103133, 15233221, 15311633, 15331931, 15333119, 16153133, 16153331, 16173133, 16331531, 16331831, 16333117, 17143331, 17311633, 17331031, 18103133

Offset: 1

G. L. Honaker, Jr., Jul 12 2005

Self-descriptive numbers are read in pairs of digits.

This uses a different method from A047841. Here the digits are described in any order, whereas in A047841 they must be described in increasing order.

			E.g. 10153331 reads "One 0, one 5, three 3's and three 1's", which does indeed describe 10153331.

Computed by Jud McCranie.
Mudge, 'Numbers Count', Personal Computer World, Jun 15 1996

Giovanni Resta, Table of n, a(n) for n = 1..10000
Prime Curios, Self-describing primes

Cf. A047841, A059504, A109775, A109776, A173101.

More terms from Giovanni Resta, Aug 14 2019

A109776 Self-describing numbers: reading the number gives a (possibly redundant) description of the number.

Original entry on oeis.org

22, 4444, 224444, 442244, 444422, 666666, 10123133, 10123331, 10143133, 10143331, 10153133, 10153331, 10163133, 10163331, 10173133, 10173331, 10183133, 10183331, 10193133, 10193331, 10212332, 10213223, 10232132

Offset: 1

Jud McCranie, Aug 15 2005

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 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)

			"22" does indeed consist of "two 2's".

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.

Cf. A108810, A173101, A005150.

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 *)

cp's OEIS Frontend

A108810 Self-describing primes.

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