cp's OEIS Frontend

A373790 The term that immediately precedes prime(n) in A373390.

%I A373790 #25 Jul 01 2024 01:54:41
%S A373790 1,2,14,6,39,11,38,17,75,62,29,117,80,88,98,165,122,59,136,207,217,
%T A373790 231,253,265,196,297,305,323,321,329,375,385,407,411,445,447,316,483,
%U A373790 495,513,531,535,555,561,573,583,621,651,669,675,687,705,711,735,753,767,785,789,801,819,825,855,889
%N A373790 The term that immediately precedes prime(n) in A373390.
%C A373790 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.
%C A373790 Conjectures:
%C A373790 (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.
%C A373790 (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.
%C A373790 (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.
%C A373790 (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.
%C A373790 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
%H A373790 Michael De Vlieger, <a href="/A373790/b373790.txt">Table of n, a(n) for n = 1..40005</a> (First 6267 terms from N. J. A. Sloane)
%e A373790 A373390(24) = 11 = prime(5), so a(5) = A373390(23) = 39.
%Y A373790 Cf. A373390, A372072, A372073, A372078-A372081, A373786-A373791.
%K A373790 nonn
%O A373790 1,2
%A A373790 _N. J. A. Sloane_, Jun 21 2024