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A079153 Primes p such that both p-1 and p+1 have at most 3 prime factors, counted with multiplicity; i.e., primes p such that bigomega(p-1) <= 3 and bigomega(p+1) <= 3, where bigomega(n) = A001222(n).

%I A079153 #24 Apr 09 2017 13:54:16
%S A079153 2,3,5,7,11,13,19,29,43,67,173,283,317,653,787,907,1867,2083,2693,
%T A079153 2803,3413,3643,3677,4253,4363,4723,5443,5717,6197,6547,6653,8563,
%U A079153 8573,9067,9187,9403,9643,10733,11443,11587,12163,12917,13997,14107,14683,15187
%N A079153 Primes p such that both p-1 and p+1 have at most 3 prime factors, counted with multiplicity; i.e., primes p such that bigomega(p-1) <= 3 and bigomega(p+1) <= 3, where bigomega(n) = A001222(n).
%C A079153 Sum of reciprocals ~ 1.495. There are 3528 primes of this kind <= 10^7.
%C A079153 From a(7) = 19 onward, this sequence is identical to A063644(n-6). - _Robin Saunders_, Sep 22 2014
%H A079153 Vincenzo Librandi, <a href="/A079153/b079153.txt">Table of n, a(n) for n = 1..1100</a>
%e A079153 907 is in the sequence because both 907-1 = 2*3*151 and 907+1 = 2*2*227 have 3 prime factors.
%p A079153 filter:= p -> isprime(p) and numtheory:-bigomega(p-1) <= 3 and numtheory:-bigomega(p+1) <= 3:
%p A079153 select(filter, [2,seq(2*i+1, i=1..10^4)]); # _Robert Israel_, Nov 11 2014
%t A079153 Select[Prime[Range[2000]],Max[PrimeOmega[#+{1,-1}]]<4&] (* _Harvey P. Dale_, Oct 07 2015 *)
%o A079153 (PARI) s(n) = {sr=0; ct=0; forprime(x=2,n, if(bigomega(x-1) < 4 && bigomega(x+1) < 4, print1(x" "); sr+=1.0/x; ct+=1; ); ); print(); print(ct" "sr); } \\ Lists primes p<=n such that both p-1 and p+1 have at most 3 prime factors.
%Y A079153 Intersection of A079150 and A079151. Cf. A079152.
%K A079153 easy,nonn
%O A079153 1,1
%A A079153 _Cino Hilliard_, Dec 27 2002