A135507 a(1) = 1; for n > 1, a(n) = 2*a(n-1) + lcm(a(n-1),n).

1, 4, 20, 60, 180, 540, 4860, 19440, 58320, 174960, 2274480, 6823440, 20470320, 184232880, 552698640, 1658095920, 31503822480, 94511467440, 283534402320, 850603206960, 7655428862640, 99520575214320, 2488014380358000

Offset: 1

Author

Benoit Cloitre, Feb 09 2008, Feb 10 2008

Keywords

• nonn
• nice

Comments

This sequence has properties related to primes and especially to twin primes. For instance a(n+1)/a(n)-2 is never the largest prime of a twin pair (except for 7).

Conjecture: Let p = a(n+1)/a(n)-2. If p is prime then p = A140460(m) or p = A140460(m) + 2 for some m. - Bill McEachen, Apr 04 2024

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A106108.

Programs

Haskell

a135507 n = a135507_list !! (n-1)
a135507_list = 1 : zipWith (+)
   (map (* 2) $ a135507_list) (zipWith lcm a135507_list [2..])
-- Reinhard Zumkeller, Mar 25 2012

Mathematica

a[1] = 1; a[n_] := a[n] = 2*a[n-1] + LCM[a[n-1], n]; Table[a[n], {n, 1, 23}] (* Jean-François Alcover, Dec 06 2012 *)
nxt[{n_,a_}]:={n+1,2a+LCM[a,n+1]}; Transpose[NestList[nxt,{1,1},30]][[2]] (* Harvey P. Dale, Oct 16 2014 *)

PARI

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