A079152 Primes p such that either p-1 or p+1 has at most 3 prime factors, counted with multiplicity; i.e., primes p such that either bigomega(p-1) <= 3 or bigomega(p+1) <= 3, where bigomega(n) = A001222(n).

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 157, 163, 167, 173, 179, 181, 191, 193, 211, 223, 227, 229, 239, 241, 257, 263, 269, 277, 281, 283, 293, 311, 313, 317, 331

Offset: 1

Author

Cino Hilliard, Dec 27 2002

Keywords

• nonn

Comments

Up to 83, this is the sequence of prime numbers A000040. 89 is not in the sequence because both 89-1 = 88 = 2*2*2*11 and 89+1 = 90 = 2*3*3*5 have 4 prime factors.

Examples

			97 is in the sequence because 97+1 = 98 = 2*7*7 has 3 prime factors.
		

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Crossrefs

Union of A079150 and A079151. Cf. A079149, A079153.

Programs

Magma

bg:=func; [2] cat [p: p in PrimesInInterval(3,340)| bg(p-1) le 3 or bg(p+1) le 3]; // Marius A. Burtea, Jan 16 2020

Mathematica

Select[Prime /@ Range[70], PrimeOmega[# - 1] <= 3 || PrimeOmega[# + 1] <= 3 & ] (* Jean-François Alcover, Jul 02 2013 *)

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 either p-1 or p+1 has at most 3 prime factors.