A136357 - OEIS

%I #10 Jul 28 2013 11:52:07

%S 4,6,9,15,30,105,210,2310,3465,15015,120120,765765,4084080,33948915,

%T 106696590,334639305,892371480,3234846615,71166625530,100280245065,

%U 200560490130,3710369067405,29682952539240,1369126185872445

%N Increasing sequence obtained by union of two sequences A136354 and {b(n)}, where b(n) is the smallest composite number m such that m+1 is prime and the set of distinct prime factors of m consists of the first n primes.

%C This sequence is different from A070826 and A118750.

%e a(4)=15 because k=2 with prime factors 3 and 5 and 15 is followed by 17, prime;

%e a(5)=30 because k=3 with prime factors 2, 3, 5 and 30 is followed by 31, prime.

%t a[n_]:=(c=Product[Prime[k],{k,n}]; For[m=1,!(!PrimeQ[c*m]&&PrimeQ[c*m+1]&& Length[FactorInteger[c*m]]==n),m++ ]; c*m);

%t b[n_]:=(c=Product[Prime[k],{k,2, n+1}]; For[m=1,!(!PrimeQ[c(2*m-1)]&&PrimeQ[c(2*m-1)+2]&&Length[FactorInteger [c(2*m-1)]]==n),m++ ]; c(2*m-1));

%t Take[Union[Table[a[k],{k,24}],Table[b[k],{k, 24}]],24] (* _Farideh Firoozbakht_, Aug 13 2009 *)

%Y Cf. A136349-A136356, A136358, A070826, A118750.

%K easy,nonn

%O 1,1

%A _Enoch Haga_, Dec 25 2007

%E Edited, corrected and extended by _Farideh Firoozbakht_, Aug 13 2009