A067024 Smallest prime p such that p+2 has exactly n distinct prime factors.

2, 13, 103, 1153, 15013, 255253, 4849843, 111546433, 4360010653, 100280245063, 5245694198743, 152125131763603, 7149881192889433, 421842990380476663, 16294579238595022363, 1106494163767990292293, 74135108972455349583763, 4632891063696575353839163, 278970415063349480483707693, 24012274383139350058948392193

Offset: 1

Author

Labos Elemer, Dec 29 2001

Keywords

• nonn

Examples

			For n = 1,...,7 the factors of 2+a(n) are as follows: 2*2, 3*5, 3*5*7, 3*5*7*11, 3*5*7*11*13, 3*5*7*11*13*17, 3*5*7*11*13*17*19; i.e., a(n) = A002110(n+1)/2 which is prime for n = 2,...,7.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..58 (terms 1..38 from Michael S. Branicky)
• Michael S. Branicky, Python program
• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A000040, A001221, A002110, A053705, A067023.

Programs

Python

# see linked program

Formula

a(n) = Min_{p in A000040 ; A001221(p+2) = n}.

Extensions

a(8)-a(15) from Donovan Johnson, Jan 21 2009

a(16) and beyond from Michael S. Branicky, Feb 07 2023