A113118 a(1) = 2. a(n) is smallest integer > a(n-1) which is a multiple of the largest prime <= a(n-1).

2, 4, 6, 10, 14, 26, 46, 86, 166, 326, 634, 1262, 2518, 5006, 10006, 19946, 39874, 79738, 159398, 318778, 637502, 1274998, 2549978, 5099902, 10199786, 20399534, 40799062, 81598082, 163196134, 326392258, 652784498, 1305568942, 2611137838

Offset: 1

Author

Leroy Quet, Jan 03 2006

Keywords

• nonn

Comments

It appears that A113117 and this sequence agree except for the 5th term.

Examples

			The greatest prime <= a(4) (= 10) is 7. The smallest multiple of 7 which is > 10 is 14. So a(5)= 14.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Mathematica

sim[n_]:=Module[{pr=If[PrimeQ[n],n,NextPrime[n,-1]]},pr*( Floor[ n/pr]+1)]; NestList[ sim,2,40] (* Harvey P. Dale, Sep 07 2012 *)

PARI

{m=33;print1(a=2,",");for(n=2,m,p=precprime(a);k=a+1;while(k%p>0,k++);print1(a=k,","))} - (Brockhaus)

Formula

a(n) = 2 * (largest prime <= a(n-1)), by Bertrand's postulate.

Extensions

a(8) to a(33) from Klaus Brockhaus, Jan 07 2006