A256383 Numbers n such that n-5 and n+5 are semiprimes.

9, 20, 30, 44, 60, 82, 90, 116, 124, 128, 138, 150, 164, 182, 208, 210, 214, 242, 254, 294, 296, 300, 304, 314, 324, 334, 360, 366, 376, 386, 398, 408, 412, 422, 432, 442, 476, 506, 510, 522, 524, 532, 538, 540, 548, 578, 584, 586, 628, 674, 676, 684

Offset: 1

Author

Michel Marcus, Mar 27 2015

Keywords

• nonn

Comments

It appears that there are no primes in this sequence.

If n is odd, one of n+5 and n-5 is divisible by 4, so unless n = 9 it can't be a semiprime. Thus all terms except 9 are even. - Robert Israel, Apr 13 2020

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358 (semiprimes).

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

Cf. A256381 (n-3 and n+3), A256382 (n-4 and n+4).

Programs

Magma

IsSemiprime:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [6..700] | IsSemiprime(n+5) and IsSemiprime(n-5) ]; // Vincenzo Librandi, Mar 29 2015

Maple

N:= 1000: # for terms <= N-5
PP:= select(isprime, {seq(i,i=3..N/3,2)}):
P:= select(`<=`,PP,floor(sqrt(N))):
SP:= {}:
for p in P do
  PP:= select(`<=`,PP,N/p);
  SP:= SP union map(`*`,PP,p);
od:
R:= {9} union (map(`+`,SP,5) intersect map(`-`,SP,5)):
sort(convert(R,list)); # Robert Israel, Apr 13 2020

Mathematica

Select[Range[2, 700], PrimeOmega[# + 5] == PrimeOmega[# - 5] == 2 &] (* Vincenzo Librandi, Mar 29 2015 *)

PARI

lista(nn,m=5) = {for (n=m+1, nn, if (bigomega(n-m)==2 && bigomega(n+m)==2, print1(n, ", ")););}

PARI

issemi(n)=bigomega(n)==2
list(lim)=my(v=List([9])); forprime(p=5,(lim-5)\3, if(issemi(3*p+10), listput(v,3*p+5))); forprime(p=29,(lim+5)\3, if(issemi(3*p-10), listput(v,3*p-5))); forstep(n=30,lim\=1,6, if(issemi(n-5) && issemi(n+5), listput(v, n))); Set(v) \\ Charles R Greathouse IV, Apr 13 2020