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A256383
Numbers n such that n-5 and n+5 are semiprimes.
4
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
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Mar 27 2015
STATUS
approved