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).

2, 3, 5, 7, 11, 13, 19, 29, 43, 67, 173, 283, 317, 653, 787, 907, 1867, 2083, 2693, 2803, 3413, 3643, 3677, 4253, 4363, 4723, 5443, 5717, 6197, 6547, 6653, 8563, 8573, 9067, 9187, 9403, 9643, 10733, 11443, 11587, 12163, 12917, 13997, 14107, 14683, 15187

Offset: 1

Author

Cino Hilliard, Dec 27 2002

Keywords

• easy
• nonn

Comments

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

From a(7) = 19 onward, this sequence is identical to A063644(n-6). - Robin Saunders, Sep 22 2014

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1100

Crossrefs

Intersection of A079150 and A079151. Cf. A079152.

Programs

Maple

filter:= p -> isprime(p) and numtheory:-bigomega(p-1) <= 3 and numtheory:-bigomega(p+1) <= 3:
select(filter, [2,seq(2*i+1, i=1..10^4)]); # Robert Israel, Nov 11 2014

Mathematica

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

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.