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

1,1

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

Mathematica

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

Crossrefs

Subsequence of A082919.

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

Sequence in context: A088846 A092208 A082919 * A252144 A201802 A233814

Adjacent sequences: A217219 A217220 A217221 * A217223 A217224 A217225

Keyword

nonn

Author

Zak Seidov, Sep 28 2012

Status

approved