A300813 - OEIS

%I #35 Jan 17 2019 22:39:25

%S 2,4,8,6,5,10,7,14,9,12,21,20,18,16,24,27,36,30,40,11,22,13,26,15,32,

%T 50,48,33,28,44,45,55,64,60,72,84,42,96,39,80,52,17,34,19,38,63,65,54,

%U 66,112,75,78,90,91,100,56,104,57,88,51,120,70,98,128,126,105,135,140,144,154,160,150,165,76,23

%N a(n) is the smallest multiple of A001414(a(n-1)) not yet seen in the sequence; a(1)=2.

%C If for some n, A001414(a(n-1)) is a prime p not seen before, then a(n)=p and a(n+1)=2*p. If the lesser of a twin prime pair is a(n), the greater is a(n+2).

%C The numbers not appearing in the first 10^7 terms are 1, 3, 37957, 37963, 38557, 39301, 40237, 40343, 40351, 40357, ...; it seems that all numbers other than 1 and 3 eventually appear. - _Charles R Greathouse IV_, Apr 09 2018

%H Michael De Vlieger, <a href="/A300813/b300813.txt">Table of n, a(n) for n = 1..10000</a>

%H Charles R Greathouse IV, <a href="/A300813/a300813.txt">Table of n, a(n) for n = 1..702396</a>

%e a(2)=4 because A001414(2)=2 and 4 is the least multiple of 2 not yet seen.

%e a(3)=8 because A001414(4)=4 and 8 is the least multiple of 4 not seen yet.

%t Nest[Append[#, Block[{k = 1, m = Total@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger@ Last@ #]}, While[! FreeQ[#, k m], k++]; k m]] &, {2}, 74] (* _Michael De Vlieger_, Mar 14 2018 *)

%o (PARI) sopfr(n,f=factor(n))=sum(i=1,#f[,1],f[i,1]*f[i,2])

%o first(n)=my(v=vector(n),s=[2],t); v[1]=2; for(m=2,n, t=sopfr(v[m-1]); forstep(k=t,t*m,t, if(setsearch(s,k), next); s=setunion(s,[k]); v[m]=k; break)); v \\ _Charles R Greathouse IV_, Apr 06 2018

%Y Cf. A001414.

%K nonn,look

%O 1,1

%A _David James Sycamore_, Mar 13 2018