A135508 - OEIS

%I #28 Sep 11 2022 21:45:15

%S 2,3,1,1,1,7,2,1,1,11,1,1,7,1,1,17,1,1,1,7,11,23,1,1,1,1,7,29,1,1,2,

%T 11,17,7,1,37,1,1,1,41,7,1,11,1,23,47,1,1,1,17,1,53,1,1,1,1,29,59,1,1,

%U 1,1,1,1,1,67,17,1,1,71,1,1,37,1,1,1,1,79,1,1,41,83,1,1,1,29,1,89,1,1,1,1

%N a(n) = x(n+1)/x(n) - 2 where x(1)=1 and x(n) = 2*x(n-1) + lcm(x(n-1),n).

%C This sequence has properties related to primes and especially to twin primes. For instance sequence consists of 1's or primes only. 2 occurs infinitely many times, largest primes in twin pairs never occur, other primes occur finitely many times...

%C For each prime p that appears in the sequence, its first appearance is at a(p-1). - _Bill McEachen_, Sep 04 2022

%H Markus Schepke, <a href="http://www.riemannhypothesis.info/wp-content/uploads/2014/10/schepke_primzahlerzeugende_folgen.pdf">Über Primzahlerzeugende Folgen</a>, Thesis, U. Hannover, 2009

%F a(2*4^k) = 2, k >= 0.

%t f[1] := 1; f[n_] := 2*f[n - 1] + LCM[f[n - 1], n]; Table[f[n + 1]/f[n] - 2, {n, 1, 10}] (* _G. C. Greubel_, Oct 16 2016 *)

%o (PARI) x1=1;for(n=2,40,x2=2*x1+lcm(x1,n);t=x1;x1=x2;print1(x2/t-2,","))

%Y Cf. A106108.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Feb 09 2008