A256383 -id:A256383 - 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, ", ")););}

A256382 Numbers n such that n-4 and n+4 are semiprimes.

Original entry on oeis.org

10, 18, 29, 30, 42, 53, 61, 73, 78, 81, 89, 90, 91, 115, 119, 125, 137, 138, 162, 165, 173, 181, 198, 205, 209, 210, 213, 217, 222, 258, 263, 291, 295, 299, 305, 323, 325, 330, 331, 390, 399, 407, 411, 441, 449, 450, 462, 477, 485, 489, 493, 497, 501, 515, 523

Offset: 1

Michel Marcus, Mar 27 2015

nonn

A117328 is the subsequence of primes.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001358 (semiprimes).
Cf. A117328 (with primes rather than semiprimes).
Cf. A124936 (n-1 and n+1), A105571 (n-2 and n+2).
Cf. A256381 (n-3 and n+3), A256383 (n-5 and n+5).

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

Select[Range[600], PrimeOmega[# + 4] == PrimeOmega[# - 4] == 2 &] (* Vincenzo Librandi, Mar 29 2015 *)
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 *)

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

A256387 Numbers n such that no prime can be the arithmetic mean of 2 semiprimes whose difference is 2*n.

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 21, 23, 25, 29, 31, 33, 35, 37, 41, 43, 45, 47, 49, 51, 53, 55, 59, 61, 63, 65, 67, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 101, 103, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 137, 139, 141, 143

Offset: 1

Michel Marcus, Mar 27 2015

nonn

That is, there is no prime p, such that p+n and p-n are both semiprime.
Complement of A256389.
From Robert Israel, Apr 13 2020: (Start)
Includes odd number n if and only if n+4 is not prime or 2*n+4 is not a semiprime.
There any no even members up to 10^5. Conjecture: all members are odd. (End)

			A256383 is the list of numbers n such that n-5 and n+5 are semiprimes, and it contains no prime, hence 5 is in the sequence.

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

Cf. A256383.

Cf. A256388 (a single prime), A256389 (one or more primes).

select(t -> not isprime(t+4) or numtheory:-bigomega(2*t+4) <> 2, [seq(i,i=1..1000,2)]); # Robert Israel, Apr 13 2020

cp's OEIS Frontend

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

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A256382 Numbers n such that n-4 and n+4 are semiprimes.

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Magma

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PARI

A256387 Numbers n such that no prime can be the arithmetic mean of 2 semiprimes whose difference is 2*n.

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Maple