Re A094405: John W. Layman's Theorem & Conjectue/Counter-Example

[zak seidov]

Hans,

At the moment,
I found record values: 

the largest  a(1)=12439, a(n>2,755,735)=688765,
the smallest a(1)=11489, a(n>2,755,735)=688765,
and a lot of a(1) between.

Up to now all seeds give the final constant -
in accord with conjecture,
and there is no known counter-example.

And I confirm your results,
which caused me to find flaw in my 
previous version of code -
thank you for this.

To avoidi duplicate calcs
(which are especially annoying in slow Mmca),
it'd be nice if interested people choose
the intervals of a(1) for searching records or
counter-examples 
(but how can one prove
that a given a(1) has no ending constant?!).

People with C++ are welcome to attack the problem.

Zak


--- Hans Havermann <pxp at rogers.com> wrote:

> On Feb 24, 2006, at 5:07 AM, zak seidov wrote:
> 
> > 2. I checked it for a(1) = 1,3,5,..,941.
> 
> > 3b. Sequences with a(1) = {449, 451, 455, 457,
> 471, 473, 475, 479}  
> > all have a(n>19207) = 4788 (record values).
> 
> I just did a quick collation of of all
> odd-numbered-seed (<2000)  
> results (stopping when I got a few identical numbers
> in a row).  
> Assuming no mistakes, the following three supersede
> the above:
> 
> * a(1) = {1123, 1127, 1129, 1133, 1135, 1137, 1139,
> 1141, 1145, 1147,  
> 1149, 1151, 1159, 1163, 1165, 1177, 1185, 1191,
> 1197, 1201, 1205,  
> 1207, 1211, 1219, 1221, 1223, 1225, 1227, 1257,
> 1261, 1275, 1279,  
> 1281, 1283, 1285, 1287, 1293, 1299, 1301, 1305,
> 1317, 1321, 1441,  
> 1551, 1553, 1555, 1559, 1565, 1567, 1569, 1571,
> 1573, 1575, 1577,  
> 1611, 1613, 1615, 1619, 1621} have a(>20647) = 5142
> 
> * a(1) = {1001, 1011, 1039, 1043, 1045, 1601, 1653,
> 1657, 1659, 1663,  
> 1667, 1669} have a(>24063) = 6001
> 
> * a(1) = {933, 939, 943, 947, 949, 1033, 1037} have
> a(>292735) = 73190
> 
> Just curious, zak... You didn't get the last result
> for 933 & 939?



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