A266845 Primes p such that p+-2 and p+-4 are semiprimes.

53, 89, 449, 683, 1259, 4283, 6803, 11789, 12781, 13553, 16561, 18593, 18899, 20287, 29303, 35099, 36217, 37619, 52163, 54181, 64763, 65213, 67103, 103769, 115831, 116009, 125551, 126541, 147997, 154043, 155161, 155609, 166013, 173699, 181943, 188911, 190261, 196613

Offset: 1

Author

Zak Seidov, Jan 04 2016

Keywords

• nonn

Examples

			a(1)=53 because 53 - 2 = 51 = 3*17, 53 + 2 = 55 = 5*11.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2500

Crossrefs

Subsequence of A063643.

Programs

Magma

IsSemiprime:=func< p | &+[ k[2]: k in Factorization(p)] eq 2 >; [p: p in PrimesInInterval(3,2*10^5)| IsSemiprime(p+2) and IsSemiprime(p+4)and IsSemiprime(p-2) and IsSemiprime(p-4)]; // Vincenzo Librandi, Jan 10 2016

Maple

filter:= proc(n) andmap(t -> numtheory:-bigomega(t)=2, [n-4,n-2,n+2,n+4]) end proc:
select(filter, [seq(ithprime(i),i=1..20000)]); # Robert Israel, Aug 11 2019

Mathematica

Select[Prime@ Range@ 18000, AllTrue[# + {-4, -2, 2, 4}, PrimeOmega@ # == 2 &] &] (* Michael De Vlieger, Jan 09 2016, Version 10 *)

PARI

lista(nn) = {forprime(p=5, nn, if (bigomega(p-4)==2 && bigomega(p+4)==2 && bigomega(p-2)==2 && bigomega(p+2)==2, print1(p, ", ")); ); } \\ Michel Marcus, Jan 10 2016