OFFSET
1,2
COMMENTS
In order for A373390 to contain a prime term, say a(i) = p, then there must be at least one earlier term which is a multiple of p, say a(j) = k*p with k>1 and j<i.
Conjectures:
(C1): For each prime p > 3, there is exactly one multiple of p that appears before p itself. Call this multiple k*p. Note that we know (see the Comments in A373390) that every prime appears in A373390. We will call this multiple k*p the term that "introduces" p.
(C2): For every prime p > 3, the introducing term k*p is always either 2*p or 3*p, and for all except the eleven primes listed in A372078 it is 2*p.
(C3): For every prime p > 3, the introducing term k*p occurs exactly 2 terms before p itself, with the single exception of A373390(11) = 7 which is introduced in A373390 three terms earlier, by A373390(8) = 14.
(C4): The primes appear in A373390 in their natural order. That is, if p<q are primes, then p appears before q. Furthermore, if k*p is the first multiple of p that appears and m*q is the first multiple of q that appears, then k*p appears before m*q.
Based on the limited number of known prime terms in the present sequence, i.e., 2, 11, 17, 29 and 59, it seems that for every a(n) that is prime, a(n) = A000040(n-1). - Ivan N. Ianakiev, Jun 22 2024
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..40005 (First 6267 terms from N. J. A. Sloane)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 21 2024
STATUS
approved