Greetings, Professor Guy, You're right in your subject line; I wouldn't believe it. I am nevertheless disappointed to find out that it isn't actually true; you seem to have been misled by some kind of editing error. Details below. At 12:45 PM 12/20/2008, you wrote:
Funsters & fansters might be amused by this somewhat unlikely coincidence. I had calculated a couple of hundred terms of a fourth order recurring sequence [it's A005178 in OEIS, if you want details] and was looking for the ranks of apparition of various primes. A 19-digit prime factor of the 53rd term turned up as a substring of the 103rd term!
any double ranks. While searching with
3140540902719737029
which is a factor of a(53),
With the indexing used in the OEIS, it's actually a(52) which equals 63389 * 3140540902719737029; no problem there.
I discovered that it's a substring of a(103):
93118232931779128686097911301602920314054090271973702981658870701 ^^^^^^^^^^^^^^^^^^^
But alas, a(102) is only 9311823293177912868609791130160292081658870701; the 19-digit prime seems to have been accidentally inserted into your copy of the number. (I'm not on all the lists you submitted your note to, so I can't reply to them all directly; thus I'm sending this only to you.) Best wishes for the holidays and the new year. -- Fred W. Helenius fredh@ix.netcom.com