A135508 a(n) = x(n+1)/x(n) - 2 where x(1)=1 and x(n) = 2*x(n-1) + lcm(x(n-1),n).

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, 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, 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

Offset: 1

Author

Benoit Cloitre, Feb 09 2008

Keywords

• nonn

Comments

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...

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

Links

• Markus Schepke, Über Primzahlerzeugende Folgen, Thesis, U. Hannover, 2009.

Crossrefs

Cf. A106108.

Programs

Mathematica

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 *)

PARI

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

Formula

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