[seqfan] Re: Idea for sequence

[carloseolivieri at hotmail.com]

Hi, FrankIt seemed an interesting case of recurrence relation to me.Questions:Is it easy to predict the next term?Is it simple to get a generating function?What is the peridiocity of the prime terms? And when n is prime too (like a(7)=47)And so on.Anyway, it was just an idea for your evaluation.Thanks in advance.Sorry for any English mistakes.Carlos
		_____________________________
From: Frank Adams-Watters <franktaw at netscape.net>
Sent: quarta-feira, junho 1, 2016 7:29 PM
Subject: [seqfan] Re: Idea for sequence
To:  <seqfan at list.seqfan.eu>


Why is this interesting?

Franklin T. Adams-Watters


-----Original Message-----
From: Carlos Eduardo Olivieri <carloseolivieri at hotmail.com>
To: seqfan <seqfan at list.seqfan.eu>
Sent: Wed, Jun 1, 2016 3:13 pm
Subject: [seqfan] Idea for sequence

Dear SeqFans
a_1 = ka_2 = qfor n > 2, a_n = greatest number j <= n^2 of the form gpf (a_(n-1)) * x + spf (a_(n-2))
gpf: greatest prime factor
spf: smallest prime factor
supposing k=2, q=3
a_3 = greatest number <= 9  of the form 3x + 2 ==> 8
a_4 = greatest number <= 16 of the form 2x + 3 ==> 15
a_5 = greatest number <= 25 of the form 5x + 2 ==> 22
a_6 = greatest number <= 36 of the form 11x + 3 ==> 36
a_7 = greatest number <= 49 of the form 3x + 2 ==> 47

2, 3, 8, 15, 22, 36, 47, ...
Best regards,Carlos
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