A136357 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.

4, 6, 9, 15, 30, 105, 210, 2310, 3465, 15015, 120120, 765765, 4084080, 33948915, 106696590, 334639305, 892371480, 3234846615, 71166625530, 100280245065, 200560490130, 3710369067405, 29682952539240, 1369126185872445

Offset: 1

Author

Enoch Haga, Dec 25 2007

Keywords

• easy
• nonn

Comments

This sequence is different from A070826 and A118750.

Examples

			a(4)=15 because k=2 with prime factors 3 and 5 and 15 is followed by 17, prime;
a(5)=30 because k=3 with prime factors 2, 3, 5 and 30 is followed by 31, prime.
		

Crossrefs

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

Programs

Mathematica

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);
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));
Take[Union[Table[a[k],{k,24}],Table[b[k],{k, 24}]],24] (* Farideh Firoozbakht, Aug 13 2009 *)

Extensions

Edited, corrected and extended by Farideh Firoozbakht, Aug 13 2009