A113117 -id:A113117 - cp's OEIS frontend

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

Leroy Quet, Jan 03 2006

nonn

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

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

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

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 *)

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

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

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

A381901 Partition the natural numbers by letting a(1)=1 (denoting the set {1}) and for n>1 define a(n) to be the least integer such that the product of the set of integers {a(n-1)+1,...,a(n)} is an integer multiple of the previous partition's product.

Original entry on oeis.org

1, 2, 4, 8, 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, 5222275634, 10444551254

Offset: 1

Andy Niedermaier, Mar 09 2025

nonn

			The first few corresponding partitions are {1}, {2}, {3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12, 13, 14}.

Cf. A006992, A090905.

Appears to agree with A113117 starting at the 5th term and with A113118 starting at the 6th term.

a(n) = A090905(n+1) - 1.

a(n) = 2 * A006992(n-1) for n>=5.

cp's OEIS Frontend

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

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