A268578 Numbers n such that n+2, n+4, n+6, n+8, n+10, n+12 and n+14 are all semiprimes.

3089, 8127, 8129, 9981, 9983, 55557, 92601, 99441, 99443, 112707, 132075, 132077, 182747, 190935, 190937, 209477, 237447, 237449, 239087, 249687, 296777, 300447, 313409, 401427, 401429, 441675, 441677, 452637, 452639, 547155, 604485, 604487, 631199, 650999

Offset: 1

Author

Vincenzo Librandi, Feb 17 2016

Keywords

• nonn

Comments

All terms are congruent to 9 or 11 (mod 18).

Examples

			8127 is in sequence because 8127+2 = 11*739, 8127+4 = 47*173, 8127+6 = 3*2711, 8127+8 = 5*1627, 8127+10 = 79*103, 8127+12 = 3*2713, 8127+14 = 7*1163 are all semiprime.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..6115

Crossrefs

Cf. A268862 (primes of the sequence).

Programs

Magma

IsSemiprime := func; [n: n in [2..700000] | forall{i: i in [2..14 by 2] | IsSemiprime(n+i)}];

Mathematica

Select[Range[400000], Union[PrimeOmega[# + {2, 4, 6, 8, 10, 12, 14}]] == {2} &]