[seqfan] Re: Cases n>9?

[israel at math.ubc.ca]

Actually I can do a bit better.  The idea is to guess some prime factors
of x, x+1 and 2*x+1, then do a search limited to numbers for which the guess
is true.  In Maple:

x0:= chrem([0,-1/2,-1],[2^4,3^4,5^4]);
for x from x0 by 2^4*3^4*5^4 do
  if numtheory:-bigomega(x) = 10 and numtheory:-bigomega(x+1)=10 and 
numtheory:-bigomega(2*x+1) = 10
    then printf("found %d\n",x); break fi
od:

found 52084090624

Cheers,
Robert


On Mar 27 2023, Allan Wechsler wrote:

>Robert, how the heck did you find that example? My toolkit is clearly
>missing a few important items.
>
>On Mon, Mar 27, 2023 at 1:12AM <israel at math.ubc.ca> wrote:
>
>> Finding the least such n may indeed be hard, but it's not that hard
>> to find one such n: e.g. 144812890624.
>>
>> Cheers,
>> Robert
>>
>> On Mar 26 2023, Allan Wechsler wrote:
>>
>> > So we are looking for a number n such that n, n+1, and 2n + 1 all have 
>> > exactly 10 prime factors, counted with multiplicity. This is obviously 
>> > quite hard; I don't see any obvious tricks that avoid brute-force 
>> > search. Anybody want to spend a bunch of CPU on this? Or are there 
>> > some shortcuts that I am missing?
>> >
>> >On Sun, Mar 26, 2023 at 10:10PM zak seidov via SeqFan <
>> >seqfan at list.seqfan.eu> wrote:
>> >
>> >> Can anyone solve cases n>9? I spend 2-3 days to no avail:( {for (m = 
>> >> 1, 10, n = 2; while (m != bigomega (n) || m != bigomega (n + 1) || m 
>> >> != bigomega (2*n + 1), n++); print (m ", " n ", "))}1, 2,2, 25,3, 
>> >> 171,4, 1592,5, 37975,6, 928624,7, 8412687,8, 106390624,9, 2306890624, 
>> >> Thx,Zak
>> >>
>> >> --
>> >> Seqfan Mailing list - http://list.seqfan.eu/
>> >>
>> >
>> >--
>> >Seqfan Mailing list - http://list.seqfan.eu/
>> >
>> >
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>--
>Seqfan Mailing list - http://list.seqfan.eu/
>
>