[seqfan] Sierpinski numbers and Riesel numbers with the same covering set

Tomasz Ordowski tomaszordowski at gmail.com
Tue Dec 26 13:06:11 CET 2023

```Dear number lovers!

Here are simple constructions of Sierpinski numbers and Riesel numbers with
the same covering sets.

If k is a Sierpinski (Riesel) number and P(k) is the product of all primes
from its covering set, then Od(P(k) + k) is also a Sierpinski (Riesel)
number with the same covering set, where Od(n) is the odd part of n.
For example, (3*5*7*13*19*37*73 + 78557) / 2^5 = 2191531 is a Sierpinski
number.
And (3*5*7*13*17*241 + 509203) / 2^3 = 762701 is a Riesel number.

If k is a Sierpinski (Riesel) number and P(k) > k is the product of
all primes from its covering set, then Od(P(k) - k) is a Riesel
(Sierpinski) number with the same covering set, where Od(n) is the odd part
of n.
For example, (3*5*7*13*19*37*73 - 78557) / 2 = 34985939 is a Riesel number.
And (3*5*7*13*17*241 - 509203) / 2 = 2541601 is a Sierpinski number.

What sequences are defined by appropriate recursions?

Happy New Year!

Tom Ordo
____________
https://oeis.org/A076336
https://oeis.org/A101036
```