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%I #59 Jul 20 2015 17:48:51
%S 102099792179230,117092756174954,136745109677256,162338633743714,
%T 167791215874866,178571623400554,183789996331514,188284244083286,
%U 211843056257854,217181576415166,224685381821406,230455538364206,234115003437666,247662164889294,265223112108514,265730468260830,266665427846390,267248859559214,268021718391414,274354628059534
%N Numbers such that it and its two neighbors are products of 8 distinct primes.
%C A subsequence of A169834.
%C With bound set at 4*10^14, the linked-to PARI program completed its run in about 2 days (producing 48 terms). The program fixes prospective smallest 4 prime factors so their product is at or above the minimum possible of the largest of 3 products of 4 primes without overlap (A260075(4)=20553), doing bound-restricted testing for the larger 4 in turn for each of these smaller quadruples. This is just one of a variety of ways of fixing a prospective trio by specifying one member as being within a certain range and satisfying the criterion. The program mostly avoids duplicates but does not entirely. See the part of the corresponding program at A259350 immediately before the print command for a fix.
%C The efficiency the program seems to generate empirically would come from the specification of product of 4 smaller primes as greater than a certain value and whole product within a certain range. Running through all even products of 8 distinct primes between the cube root of the (3n)-th primorial and the bound given would be a simpler way but one not so statistically limited (with a proportionally larger number of candidates). Note: The author is not making a claim of maximal efficiency, just of marked improvements over some simpler approaches.
%C a(1)=A093550(8).
%H James G. Merickel, <a href="/A259801/b259801.txt">Table of n, a(n) for n = 1..48</a>
%H James G. Merickel, <a href="https://oeis.org/w/images/4/49/Mer8a.txt">PARI program</a>
%e 102099792179229=3*13*19*53*83*131*181*1321, 102099792179230=2*5*17*43*127*229*283*1697, and 102099792179231=7*11*23*29*31*71*113*7993. No smaller collection meets the criterion, so a(1)=102099792179230.
%o See above link to PARI program generating terms under 4*10^14 (out of order and with some duplicates).
%Y Cf. A093550, A169834, A248201, A248202, A248203, A248204, A259349, A259350, A260075.
%K nonn
%O 1,1
%A _James G. Merickel_, Jul 14 2015
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