cp's OEIS Frontend

If n > 2, then a(n) = product of n-1 consecutive distinct prime divisors. E.g. a(5)=210, the product of 4 consecutive and distinct prime divisors, 2,3,5,7. - Enoch Haga, Dec 08 2007

From Bill McEachen, Jul 10 2022: (Start)

Rather than have code merely generating the conjectured values, one can compare values of sequence terms at the same position n. Specifically, locate new maximums where (p,p+even) are both prime, where even=2,4,6,8,... and the datum set is taken with even=4. A new maximum implies a new jumping champion.

Doing this produces the terms 2,4,6,30,210,2310,30030,.... Looking at the plot of a(n) ratio for gap=2/gap=6, the value changes VERY slowly, and is 2.14 after 50 million terms (one can see the trend via Plot 2 of A001359 vs A023201 (3rd option seqA/seqB vs n). The ratio for gap=4/gap=2 ~ 1, implying they are equally frequent. (End)

A number is called a jumping champion for n, if it is the most frequently occurring difference between consecutive primes <= n;

there are occasionally several jumping champions: see A087102; A087103(n) is the smallest jumping champion for prime(n);

a(n)<=6 for small n, see Odlyzko et al. for primes>1.7*10^35.

For small n: a(n)<=3; A087103(n) and A087104(n) give the smallest and greatest jumping champion(s) for prime(n).