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

1,1

Comments

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

Links

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

Formula

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

Example

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

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 *)

Prog

(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)

Crossrefs

Sequence in context: A280611 A138016 A239787 * A287636 A032417 A152415

Adjacent sequences: A113115 A113116 A113117 * A113119 A113120 A113121

Keyword

nonn

Author

Leroy Quet, Jan 03 2006

Extensions

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

Status

approved