[seqfan] A hopeless problem and a specific question

[Tomasz Ordowski]

Dear readers,

I have an extremely hard problem:

Are there (odd) positive integers k such that
|k-2^m| is a Sierpinski number for every m>0
and k+2^m is a Riesel number for every m>0
?

Common sense tells me that ...
Conjecture: such numbers k do not exist.
However, math often goes beyond common sense!
Cf. https://oeis.org/A076335 (the Brier numbers).
See https://oeis.org/A076336/a076336b.html

The concrete question: Are there pairs of S and R,
where S is a Sierpinski number and R is a Riesel number,
such that |S-R| or S+R is a power of 2 ?
For S in https://oeis.org/A076336
For R in https://oeis.org/A101036
Happy searches!

Greetings from Poland,

Thomas Ordowski