A256382 -id:A256382 - cp's OEIS frontend

A256381 Numbers n such that n-3 and n+3 are semiprimes.

7, 12, 18, 36, 52, 54, 88, 90, 118, 126, 158, 180, 206, 212, 216, 218, 250, 256, 262, 292, 298, 302, 306, 324, 326, 332, 338, 358, 368, 374, 410, 414, 448, 450, 508, 514, 530, 532, 540, 548, 556, 562, 576, 586, 594, 626, 632, 652, 682, 684, 692, 700, 710, 720

Offset: 1

Michel Marcus, Mar 27 2015

nonn

All but the first term are even.

Cf. A001358 (semiprimes).
Cf. A124936 (n-1 and n+1), A105571 (n-2 and n+2).
Cf. A256382 (n-4 and n+4), A256383 (n-5 and n+5).

IsSemiprime:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [4..750] | IsSemiprime(n+3) and IsSemiprime(n-3) ]; // Vincenzo Librandi, Mar 28 2015

Select[Range[750], PrimeOmega[# + 3] == PrimeOmega[# - 3] == 2 &] (* Vincenzo Librandi, Mar 28 2015 *)
SequencePosition[Table[If[PrimeOmega[n]==2,1,0],{n,800}],{1,,,_,,,1}][[All,1]]+3 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 21 2017 *)

lista(nn,m=3) = {for (n=m+1, nn, if (bigomega(n-m)==2 && bigomega(n+m)==2, print1(n, ", ")););}

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

Original entry on oeis.org

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

Michel Marcus, Mar 27 2015

nonn

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

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

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).

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

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

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

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

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

A256389 Numbers n such that one or more primes can be the arithmetic mean of 2 semiprimes whose difference is 2*n.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 22, 24, 26, 27, 28, 30, 32, 34, 36, 38, 39, 40, 42, 44, 46, 48, 50, 52, 54, 56, 57, 58, 60, 62, 64, 66, 68, 69, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110

Offset: 1

Michel Marcus, Mar 27 2015

nonn

That is, there are several primes p, such that p+n and p-n are both semiprime.
Complement of A256387.
The terms of this sequence that do not belong to A256388 are even.

			A256381 is the list of numbers n such that n-3 and n+3 are semiprimes, and it contains a single prime, hence 3 is in the sequence.
A256382 is the list of numbers n such that n-4 and n+4 are semiprimes, and it contains several primes, hence 4 is in the sequence.

Cf. A124936, A105571, A256382.

Cf. A256387 (no prime), A256388 (a single prime).

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A256381 Numbers n such that n-3 and n+3 are semiprimes.

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

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A256389 Numbers n such that one or more primes can be the arithmetic mean of 2 semiprimes whose difference is 2*n.

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