A280740 - OEIS

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).

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, 19, 23, 23, 23, 25, 25, 25, 25, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 37, 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

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OFFSET

1,1

COMMENTS

We use the convention that an empty product is 1.

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.)

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.

The conjecture is true for n up to 10^7. - Lars Blomberg Jan 14 2017

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

CROSSREFS

Cf. A280864, A280738, A280741, A280742, A280743, A280744.