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Smallest prime p such that p+2 has exactly n distinct prime factors.
8

%I #27 Nov 30 2023 23:16:54

%S 2,13,103,1153,15013,255253,4849843,111546433,4360010653,100280245063,

%T 5245694198743,152125131763603,7149881192889433,421842990380476663,

%U 16294579238595022363,1106494163767990292293,74135108972455349583763,4632891063696575353839163,278970415063349480483707693,24012274383139350058948392193

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

%H Sean A. Irvine, <a href="/A067024/b067024.txt">Table of n, a(n) for n = 1..58</a> (terms 1..38 from Michael S. Branicky)

%H Michael S. Branicky, <a href="/A067024/a067024.py.txt">Python program</a>

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a067/A067024.java">Java program</a> (github)

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

%e 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.

%o (Python) # see linked program

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

%K nonn

%O 1,1

%A _Labos Elemer_, Dec 29 2001

%E a(8)-a(15) from _Donovan Johnson_, Jan 21 2009

%E a(16) and beyond from _Michael S. Branicky_, Feb 07 2023