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

1,1

Links

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

Subsequence of A063643.

Sequence in context: A137869 A096697 A033234 * A238678 A380961 A142296

Adjacent sequences: A266842 A266843 A266844 * A266846 A266847 A266848

Keyword

nonn

Author

Zak Seidov, Jan 04 2016

Status

approved