A259801 Numbers such that it and its two neighbors are products of 8 distinct primes.

102099792179230, 117092756174954, 136745109677256, 162338633743714, 167791215874866, 178571623400554, 183789996331514, 188284244083286, 211843056257854, 217181576415166, 224685381821406, 230455538364206, 234115003437666, 247662164889294, 265223112108514, 265730468260830, 266665427846390, 267248859559214, 268021718391414, 274354628059534

Offset: 1

Author

James G. Merickel, Jul 14 2015

Keywords

• nonn

Comments

A subsequence of A169834.

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.

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.

a(1)=A093550(8).

Examples

			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.
		

Links

• James G. Merickel, Table of n, a(n) for n = 1..48
• James G. Merickel, PARI program

Crossrefs

Cf. A093550, A169834, A248201, A248202, A248203, A248204, A259349, A259350, A260075.

Programs

PARI

\\ See above link to PARI program generating terms under 4*10^14 (out of order and with some duplicates).