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

Author

Michel Marcus, Mar 27 2015

Keywords

• nonn

Comments

All but the first term are even.

Crossrefs

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).

Programs

Magma

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

Mathematica

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 *)

PARI

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