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%I #31 Apr 18 2023 09:42:47
%S 2,3,5,7,11,13,23,37,47,59,61,73,83,107,157,167,179,193,227,263,277,
%T 313,347,359,383,397,421,457,467,479,503,541,563,587,613,661,673,719,
%U 733,757,839,863,877,887,983,997,1019,1093,1153,1187,1201,1213,1237
%N 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 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 Primes which are not the sum of two consecutive composite numbers. - _Juri-Stepan Gerasimov_, Nov 15 2009
%t Select[Prime[Range[500]],MemberQ[PrimeOmega[{#-1,#+1}],2]&] (* _Harvey P. Dale_, Sep 04 2011 *)
%o (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 Union of A079147 and A079148. Cf. A060254, A079152.
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Dec 27 2002
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