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

1,1

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

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 *)

Prog

(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
(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

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).

Sequence in context: A050682 A094196 A253089 * A322433 A017497 A059108

Adjacent sequences: A256380 A256381 A256382 * A256384 A256385 A256386

Keyword

nonn

Author

Michel Marcus, Mar 27 2015

Status

approved