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

1,1

Comments

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

Links

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

Example

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.

Mathematica

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

Prog

(Magma) IsSemiprime := func<n | &+[m[2]: m in Factorization(n)] eq 2>; [n: n in [2..700000] | forall{i: i in [2..14 by 2] | IsSemiprime(n+i)}];

Crossrefs

Cf. A268862 (primes of the sequence).

Sequence in context: A234781 A045079 A195811 * A268862 A277786 A092129

Adjacent sequences: A268575 A268576 A268577 * A268579 A268580 A268581

Keyword

nonn

Author

Vincenzo Librandi, Feb 17 2016

Status

approved