cp's OEIS Frontend

A280740 After S(n)=A280864(n) has been computed, let p(n) = product of distinct primes shared by S(n-1) and S(n); let q(n) = product of distinct primes in S(n) but not in S(n-1); and let r(n) = smallest number not yet in S. Sequence gives r(n).

%I A280740 #34 Dec 27 2020 19:41:47
%S A280740 2,3,3,5,5,5,7,7,7,7,11,11,11,13,13,13,13,13,13,13,13,13,17,19,19,19,
%T A280740 19,23,23,23,25,25,25,25,29,29,29,29,31,31,31,31,31,31,31,31,31,31,37,
%U A280740 37,37,37,37,37,41,41,41,41,41,41,41,41,43,43,43,47,47,47,47,53,53,53,53,53,53,53,53,53,53
%N A280740 After S(n)=A280864(n) has been computed, let p(n) = product of distinct primes shared by S(n-1) and S(n); let q(n) = product of distinct primes in S(n) but not in S(n-1); and let r(n) = smallest number not yet in S. Sequence gives r(n).
%C A280740 We use the convention that an empty product is 1.
%C A280740 By decree, gcd(S(n+1),p(n)) = 1, gcd(S(n+1),q(n)) = q(n) = p(n+1), S(n+1) >= r(n). (Note p(n) is as defined above; it is not the n-th prime.)
%C A280740 Conjecture: except for the four terms equal to 25, a(n) is always a prime, and all the primes appear and in their natural order.
%C A280740 The conjecture is true for n up to 10^7. - _Lars Blomberg_ Jan 14 2017
%H A280740 N. J. A. Sloane, <a href="/A280740/b280740.txt">Table of n, a(n) for n = 1..10000</a>
%Y A280740 Cf. A280864, A280738, A280741, A280742, A280743, A280744.
%K A280740 nonn
%O A280740 1,1
%A A280740 _N. J. A. Sloane_, Jan 12 2017