

A268578


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


2



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
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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



