A217222 Initial terms of sets of 8 consecutive semiprimes with gap 2.

8129, 237449, 401429, 452639, 604487, 858179, 1471727, 1999937, 2376893, 2714987, 3111977, 3302039, 3869237, 4622087, 7813559, 9795449, 10587899, 10630739, 11389349, 14186387, 14924153, 15142547, 15757337, 18017687, 18271829, 19732979, 22715057, 25402907

Offset: 1

Author

Zak Seidov, Sep 28 2012

Keywords

• nonn

Comments

All terms == 11 (mod 18).

Also all terms of sets of 8 consecutive semiprimes are odd, e.g., {8129, 8131, 8133, 8135, 8137, 8139, 8141, 8143} is the smallest set of 8 consecutive semiprimes.

Note that in all cases "9th term" (in this case 8143+2=8145) is divisible by 9 and hence is not semiprime.

Also note that all seven "intermediate" even integers (in this case {8130, 8132, 8134, 8136, 8138, 8140, 8142}) have at least three prime factors counting with multiplicity. Up to n = 40*10^9 there are 5570 terms of this sequence.

Links

• Zak Seidov, Table of n, a(n) for n = 1..5570

Crossrefs

Subsequence of A082919.

Cf. A056809, A070552, A092125-A092129, A092207-A092209.

Programs

Mathematica

Transpose[Select[Partition[Select[Range[26*10^6],PrimeOmega[#] == 2&],8,1], Union[ Differences[#]]=={2}&]][[1]] (* Harvey P. Dale, Sep 02 2015 *)