[seqfan] Re: Number names - a chain

[Bob Selcoe]

Nice!

It would be interesting to see how many variations there are of these 
longer-length sequences.  For example, for length 23, we could use this 
sequence replacing 40 with 42 or 44, or 0 with 40 and 40 with 44, or 2000 
with 2002,  or 0 with {3, 10, 12, 14, 20, 21, 22, 23, 24, 41, 42, 43, 44, 
101, 102...}

Best,
Bob S.
--------------------------------------------------
From: "Sean A. Irvine" <sairvin at gmail.com>
Sent: Tuesday, March 10, 2015 2:53 PM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Number names - a chain

> Before I read Hans' excellent description, my program made it to 23 
> numbers:
>
> 0, 6, 1, 30, 7, 32, 11, 40, 9, 4, 60, 100, 56, 101, 66, 111, 50, 700,
> 52, 707, 2, 5, 2000
>
> On 10 March 2015 at 19:06, Hans Havermann <gladhobo at teksavvy.com> wrote:
>> Sean A. Irvine: "Still running, but I've found one of length 17 so far."
>>
>> SeqFan dealt with the subject on the 6th & 7th of July, 2011. At the time 
>> Douglas McNeil suggested 5, 2, 9, 40, 11, 36, 1, 30, 7, 44, 6, 12, 4, 66, 
>> 101, 56, 100, 50, 0, 60, 104, which I told him could be preceded by 2000 
>> (for a total length of 22). In posing the query, Eric Angelini had come 
>> up with a 15-element chain compared to the 13 he submitted this time 
>> around. ;)
>>
>> I did set up a brute force attack in a private email to Eric Angelini, 
>> Douglas McNeil, Claudio Meller, and Maximilian Hasler which is worth 
>> repeating if anyone wants to have a go at it:
>>
>> "While I suggested that there were 181 numbers in the connectible (at 
>> least one neighbour) universe, 144 of these have only one neighbour and, 
>> to the extent that these necessarily represent chain end-points, 137 of 
>> them may be culled in favour of a representative from their seven (2, 3, 
>> 4, 5, 6, 11, 50) sinks. Thus,
>>
>> 500 will represent any of {505, 506, 507, 509, 511, 600, 605, 606, 607, 
>> 609, 611, 705, 706, 709, 900, 905, 906, 907, 909, 911}
>>
>> 6000000 will represent any of {6000006, 6000000000, 6000000006, 
>> 6006000000, 6006000006, 6000000000000000000000000000000, 
>> 6000000000000000000000000000006, 6000000000000000000000006000000, 
>> 6000000000000000000000006000006, 6000000000000000000006000000000, 
>> 6000000000000000000006000000006, 6000000000000000000006006000000, 
>> 6000000000000000000006006000006}
>>
>> 8 will represent any of {16, 17, 18, 19, 26, 27, 28, 29, 67, 68, 69, 70, 
>> 76, 77, 78, 79, 80, 86, 87, 88, 89, 90, 96, 97, 98, 99}
>>
>> 2000 will represent {2002}
>>
>> 14 will represent any of {21, 22, 23, 24, 41, 43, 102, 103, 110, 112, 
>> 114, 120, 121, 122, 123, 124, 140, 141, 142, 143, 144, 200, 201, 202, 
>> 203, 204, 210, 211, 212, 214, 220, 221, 222, 223, 224, 240, 241, 242, 
>> 243, 244, 300, 301, 302, 303, 304, 310, 311, 312, 314, 320, 321, 322, 
>> 323, 324, 340, 341, 342, 343, 344, 402, 403, 410, 412, 414, 420, 421, 
>> 422, 423, 424, 440, 441, 442, 443, 444}
>>
>> 46 will represent either of {62, 64}
>>
>> 107 will represent {701}
>>
>>
>> This cull leaves us with just 44 numbers:
>>
>> {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 20, 30, 32, 34, 36, 40, 
>> 42, 44, 46, 50, 52, 54, 56, 60, 66, 100, 101, 104, 107, 111, 400, 401, 
>> 404, 411, 500, 700, 707, 711, 2000, 6000000}
>>
>> ... with the following corresponding sets of neighbours:
>>
>> {{6, 50, 56, 60, 66}, {6, 30, 36, 50, 56, 60, 66}, {5, 6, 7, 9, 11, 500, 
>> 700, 707, 711}, {6, 6000000}, {6, 7, 8, 9, 10, 11, 12, 20, 60, 66}, {2, 
>> 2000}, {0, 1, 2, 3, 4, 10, 11, 12, 14, 20, 40, 42, 44, 100, 101, 104, 
>> 111, 400, 401, 404, 411}, {2, 4, 30, 32, 34, 40, 42, 44, 50, 52, 54}, 
>> {4}, {2, 4, 40, 42, 44}, {4, 6}, {2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 
>> 46, 50, 52, 54, 56, 60, 66}, {4, 6}, {6}, {4, 6}, {1, 7, 11}, {7, 11}, 
>> {7, 11}, {1, 11}, {6, 7, 9, 11}, {6, 7, 9, 11}, {6, 7, 9, 11}, {11}, {0, 
>> 1, 7, 11, 100, 101, 107, 111, 700, 707, 711}, {7, 11, 700, 707, 711}, {7, 
>> 11}, {0, 1, 11, 100, 101, 111}, {0, 1, 4, 11, 100, 101, 104, 111, 400, 
>> 401, 404, 411}, {0, 1, 4, 11, 100, 101, 104, 111, 400, 401, 404, 411}, 
>> {6, 50, 56, 60, 66}, {6, 50, 56, 60, 66}, {6, 60, 66}, {50}, {6, 50, 56, 
>> 60, 66}, {6, 60, 66}, {6, 60, 66}, {6, 60, 66}, {6, 60, 66}, {2}, {2, 50, 
>> 52}, {2, 50, 52}, {2, 50, 52}, {5}, {3}}"
>>
>>
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