1,1

Start of a cluster of 8 consecutive semiprimes. Semiprimes in arithmetic progression. All terms are odd, see also A056809.

Note that there cannot exist 9 consecutive odd semiprimes. Out of any 9 consecutive odd numbers, one of them will be divisible by 9. The only multiple of 9 which is a semiprime is 9 itself, and it is easy to see that's not part of a solution. - Jack Brennen (jb(AT)brennen.net), Jan 04 2006

For the first 500 terms, a(n) is roughly 40000*n^1.6, so the sequence appears to be infinite. Note that (a(n)+4)/3 and (a(n)+10)/3 are twin primes. - Don Reble, Jan 05 2006.

Author of this sequence is Jack Brennen (jb(AT)brennen.net), who provided the terms up to 991289 in a posting to the seqfan mailing list on April 5, 2003

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

a(1)=8129 because 8129=11*739, 8131=47*173, 8133=3*2711, 8135=5*1627, 8137=79*103, 8139=3*2713, 8141=7*1163, 8143=17*479 are semiprimes.

PrimeFactorExponentsAdded[n_] := Plus @@ Flatten[Table[ #[[2]], {1}] & /@ FactorInteger[n]]; Select[ Range[3*10^6], PrimeFactorExponentsAdded[ # ] == PrimeFactorExponentsAdded[ # + 2] == PrimeFactorExponentsAdded[ # + 4] == PrimeFactorExponentsAdded[ # + 6] == PrimeFactorExponentsAdded[ # + 8] == PrimeFactorExponentsAdded[ # + 10] == PrimeFactorExponentsAdded[ # + 12] == PrimeFactorExponentsAdded[ # + 14] == 2 &] - Robert G. Wilson v (rgwv(AT)rgwv.com) and Zak Seidov (zakseidov(AT)yahoo.com), Feb 24 2004

Cf. A001358, A082130, A082131.

Cf. A056809, A070552, A092207, A092125, A092126, A092127, A092128, A092129, A092209.

Sequence in context: A025306 A088846 A092208 this_sequence A013689 A109145 A096329

Adjacent sequences: A082916 A082917 A082918 this_sequence A082920 A082921 A082922

nonn

Hugo Pfoertner (hugo(AT)pfoertner.org), Apr 22 2003