[seqfan] Re: Self-Parity/Antiparity Sequences & Numbers

[Alois Heinz]

Hello Éric,

S =     1, 11, 12, 22, 111, 113, 121, 122, 123, 131, 133,
    222, 223, 311, 313, 321, 323, 331, 333, 1111,
    1113, 1114, 1131, 1133, 1134, 1144, 1211, 1212,
    1213, 1214, 1221, 1222, 1224, 1231, 1232, 1233,
    1234, 1242, 1244, 1311, 1313, 1314, 1331, 1333,
    1334, 1412, 1414, 1422, 1424, 1432, 1434, 1442,
    1444, 2222, 2224, 2232, 2233, 2234, 2242, 2244,
    2422, 2424, 2432, 2434, 2442, 2444, 3111, 3113,
    3114, 3131, 3133, 3134, 3211, 3212, 3213, 3214,
    3231, 3232, 3233, 3234, 3311, 3313, 3314, 3331,
    3333, 3334, 3412, 3414, 3432, 3434, 4222, 4224,
    4232, 4234, 4242, 4244, 4334, 4422, 4424, 4432,
    4434, 4442, 4444, 11111, 11113, 11115, 11131,
    11133, 11135, 11141, 11143, 11144, 11145, 11151,
    11153, 11155, 11311, 11313, 11315, 11331, 11333,
    11335, 11341, 11343, 11344, 11345, 11351, 11353,
    11355, 11441, 11444, 11445, 11511, 11513, 11515,
    11531, 11533, 11535, 11541, 11543, 11545, 11551,
    11553, 11555, 12111, 12112, 12113, 12115, 12121,
    12122, 12123, 12124, 12125, 12131, 12132, 12133,
    12135, 12141, 12142, 12143, 12144, 12145, 12151,
    12153, 12155, 12211, 12212, 12215, 12221, 12222,
    12224, 12225, 12241, 12242, 12244, 12245, 12251,
    12255, 12311, 12312, 12313, 12315, 12321, 12322,
    12323, 12324, 12325, 12331, 12332, 12333, 12335,
    12341, 12342, 12343, 12344, 12345, 12351, 12353,
    12355, 12421, ...

Alois

Eric Angelini schrieb:
> Hello SeqFans, 
>  
> 321 is a "self-parity number".
>   Its first digit, 3, says: - the 3rd digit has my parity
>                                (which is true, "1" is odd as "3" is)
>   Its second digit, 2, says: - the 2nd digit has my parity
>                                (which is true, "2" and "2" are even)
>   Its third digit, 1, says: - the 1st digit has my parity
>                                (which is true, "3" is odd as "1" is)
>  
> A "self-parity number" is a number whose digit 'speak' and assert
> true statements about their parity.
>  
> The sequence of such self-parity numbers seems to start like this:
>  
> S = 1, 11, 12, 22, 111, 113, 121, 122, 123, 131, 133, 222, 311, 313,
>     321, 323, 331, 333, 1111, 1113, 1131, ...
>
> (this is not http://www.research.att.com/~njas/sequences/A105945)
>  
> Could someone please check and compute a hundred terms more or so?
> __________
>
> More on the same topic, here:
> http://www.cetteadressecomportecinquantesignes.com/ParitySeq.htm
>
> The last seq on the above page is a nightmare to compute by hand :-(
>
> Best,
> É.
>
>
>
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