Re A094405: John W. Layman's Theorem & Conjection

[Hans Havermann]

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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