cp's OEIS Frontend

A079149 Primes p such that either p-1 or p+1 has at most 2 prime factors, counted with multiplicity; i.e., primes p such that either bigomega(p-1) <= 2 or bigomega(p+1) <= 2, where bigomega(n) = A001222(n).

%I A079149 #31 Apr 18 2023 09:42:47
%S A079149 2,3,5,7,11,13,23,37,47,59,61,73,83,107,157,167,179,193,227,263,277,
%T A079149 313,347,359,383,397,421,457,467,479,503,541,563,587,613,661,673,719,
%U A079149 733,757,839,863,877,887,983,997,1019,1093,1153,1187,1201,1213,1237
%N A079149 Primes p such that either p-1 or p+1 has at most 2 prime factors, counted with multiplicity; i.e., primes p such that either bigomega(p-1) <= 2 or bigomega(p+1) <= 2, where bigomega(n) = A001222(n).
%C A079149 There are only 2 primes such that both p-1 and p+1 have at most 2 prime factors - 3 and 5. Proof: If p > 5 then whichever of p-1 and p+1 is divisible by 4 has at least 3 prime factors.
%C A079149 Primes which are not the sum of two consecutive composite numbers. - _Juri-Stepan Gerasimov_, Nov 15 2009
%t A079149 Select[Prime[Range[500]],MemberQ[PrimeOmega[{#-1,#+1}],2]&] (* _Harvey P. Dale_, Sep 04 2011 *)
%o A079149 (PARI) s(n) = {sr=0; ct=0; forprime(x=2,n, if(bigomega(x-1) < 3 || bigomega(x+1) < 3, print1(x" "); sr+=1.0/x; ct+=1; ); ); print(); print(ct" "sr); } \\ Lists primes p<=n such that p+-1 has at most 2 prime factors.
%Y A079149 Union of A079147 and A079148. Cf. A060254, A079152.
%K A079149 easy,nonn
%O A079149 1,1
%A A079149 _Cino Hilliard_, Dec 27 2002