A256382 - OEIS

%I #14 Sep 08 2022 08:46:11

%S 10,18,29,30,42,53,61,73,78,81,89,90,91,115,119,125,137,138,162,165,

%T 173,181,198,205,209,210,213,217,222,258,263,291,295,299,305,323,325,

%U 330,331,390,399,407,411,441,449,450,462,477,485,489,493,497,501,515,523

%N Numbers n such that n-4 and n+4 are semiprimes.

%C A117328 is the subsequence of primes.

%H Harvey P. Dale, <a href="/A256382/b256382.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Range[600], PrimeOmega[# + 4] == PrimeOmega[# - 4] == 2 &] (* _Vincenzo Librandi_, Mar 29 2015 *)

%t Flatten[Position[Partition[Table[If[PrimeOmega[n]==2,1,0],{n,600}],9,1],_?(#[[1]]==#[[9]]==1&),{1},Heads->False]]+4 (* _Harvey P. Dale_, Mar 29 2015 *)

%o (PARI) lista(nn,m=4) = {for (n=m+1, nn, if (bigomega(n-m)==2 && bigomega(n+m)==2, print1(n, ", ")););}

%o (Magma) IsSemiprime:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [6..750] | IsSemiprime(n+4) and IsSemiprime(n-4) ]; // _Vincenzo Librandi_, Mar 29 2015

%Y Cf. A001358 (semiprimes).

%Y Cf. A117328 (with primes rather than semiprimes).

%Y Cf. A124936 (n-1 and n+1), A105571 (n-2 and n+2).

%Y Cf. A256381 (n-3 and n+3), A256383 (n-5 and n+5).

%K nonn

%O 1,1

%A _Michel Marcus_, Mar 27 2015