A079153 - OEIS

%I #24 Apr 09 2017 13:54:16

%S 2,3,5,7,11,13,19,29,43,67,173,283,317,653,787,907,1867,2083,2693,

%T 2803,3413,3643,3677,4253,4363,4723,5443,5717,6197,6547,6653,8563,

%U 8573,9067,9187,9403,9643,10733,11443,11587,12163,12917,13997,14107,14683,15187

%N 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 Sum of reciprocals ~ 1.495. There are 3528 primes of this kind <= 10^7.

%C From a(7) = 19 onward, this sequence is identical to A063644(n-6). - _Robin Saunders_, Sep 22 2014

%H Vincenzo Librandi, <a href="/A079153/b079153.txt">Table of n, a(n) for n = 1..1100</a>

%e 907 is in the sequence because both 907-1 = 2*3*151 and 907+1 = 2*2*227 have 3 prime factors.

%p filter:= p -> isprime(p) and numtheory:-bigomega(p-1) <= 3 and numtheory:-bigomega(p+1) <= 3:

%p select(filter, [2,seq(2*i+1, i=1..10^4)]); # _Robert Israel_, Nov 11 2014

%t Select[Prime[Range[2000]],Max[PrimeOmega[#+{1,-1}]]<4&] (* _Harvey P. Dale_, Oct 07 2015 *)

%o (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 Intersection of A079150 and A079151. Cf. A079152.

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Dec 27 2002