A052215 a(n) = smallest number m such that m and m+1 are the product of exactly n distinct primes.

2, 14, 230, 7314, 378014, 11243154, 965009045, 65893166030, 5702759516090, 605247139068494, 78971815814237709, 22593106657425552170

Offset: 1

Author

Erich Friedman, Jan 29 2000

Keywords

• hard
• nice
• nonn
• more

Comments

Prime factors may not be repeated in m and m+1. The difference between this sequence and A093548 is that in the latter, prime factors may be repeated. So the present sequence imposes more stringent conditions than A093548, hence a(n) >= A093548(n). - N. J. A. Sloane, Nov 21 2015

A115186(n) <= A093548(n) <= a(n). - Zak Seidov, Jan 16 2015

2^63 < a(12) <= 22593106657425552170. [Donovan Johnson, Oct 23 2008]

a(12) confirmed to be the upper limit of the range above. - Bert Dobbelaere, Jun 27 2019

Examples

			14 and 15 are both the product of 2 primes.
230 is the 3rd entry because we have (230=2*5*23, 231=3*7*11).
		

Crossrefs

Cf. A093548 (another version), A093549, A093550, A115186, A318896.

Subsequence of A005117.

Extensions

More terms from Naohiro Nomoto, Jul 08 2001

a(7) from Farideh Firoozbakht, Apr 06 2004

a(8)-a(10) from Martin Fuller, Jan 17 2006

a(11) from Donovan Johnson, Oct 23 2008

a(12) from Bert Dobbelaere, Jun 27 2019