## Wednesday, March 16, 2022

### Numbers that are products of distinct primorial numbers

I'm officially credited with a number sequence.

https://oeis.org/A129912

 A129912 Numbers that are products of distinct primorial numbers (see A002110). 22
 1, 2, 6, 12, 30, 60, 180, 210, 360, 420, 1260, 2310, 2520, 4620, 6300, 12600, 13860, 27720, 30030, 37800, 60060, 69300, 75600, 138600, 180180, 360360, 415800, 485100, 510510, 831600, 900900, 970200, 1021020, 1801800, 2910600, 3063060, 5405400
 OFFSET 1,2 COMMENTS Conjecture: every odd prime p is either adjacent to a term of A129912 or a prime distance q from some term of A129912, where q < p. - Bill McEachen, Jun 03 2010, edited for clarity in Feb 26 2019The first 2^20 terms k > 2 of A283477 all satisfy also the condition that the differences k-A151799(k) and A151800(k)-k are always either 1 or prime, like is also conjectured to hold for A002182 (cf. also the conjecture given in A117825). However, for A025487, which is a supersequence of both sequences, this is not always true: 512 is a member of A025487, but A151800(512) = 521, with 521 - 512 = 9, which is a composite number. - Antti Karttunen, Feb 26 2019 REFERENCES CRC Standard Mathematical Tables, 28th Ed., CRC Press LINKS T. D. Noe and Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)Bill McEachen, Normalized A129912Robert Potter, Primorial Conjecture.J. Sokol, Sokol's Prime ConjectureWikipedia, PrimorialIndex entries for sequences related to primorial numbers