various items

[djr at nk.ca]

> An old sequence which I cannot understand.  Could someone please
> provide a clear definition?  
> %S A084924 3,7,31,127,1279,3583,5119,6143,8191

Perhaps the author intends this:

    Let t(x) be the highest power of two which divides x+1. Then
    a(1)=3;
    a(n) is the least prime of the form
        (2*k+1)*t(a(n-1)) + a(n-1)
    (where k is any positive integer).

> First define Riesel primes as k*2^n-1, with k < 2^n.
Well, maybe that definition produces a non-Riesel prime, but it's pretty
unlikely.

Anyway, that's equivalent to this simpler definition:

    Let t(x) be the highest power of two which divides x+1. Then
    a(1)=3;
    a(n) is the least prime p for which t(p) > t(a(n-1)).

So I'd put it this way.

%I A084924
%S A084924 3,7,31,127,1279,3583,5119,6143,8191,81919,131071,524287,
%T A084924 14680063,109051903,654311423,738197503,2147483647,
%U A084924 21474836479,51539607551,824633720831,13743895347199
%N A084924 Let t(x) be the highest power of two which divides x+1. Then a(1)=3; a(n) is the least prime p for which t(p) > t(a(n-1)).
%e A084924 a(5)=1279, because t(a(4))=7, and 1279 is the least prime with t(p)>7.
%K A084924 nonn
%O A084924 1,1
%A A084924 Shane Findley (TTcreation(AT)aol.com), Jul 15 2003
%E A084924 Edited by Don Reble (djr(AT)nk.ca), Apr 08 2004

--
Don Reble       djr at nk.ca