[seqfan] Re: Nice conjecture from Enrique Navarrete re divisors of triangular numbers A111273

[Fred Lunnon]

  Uh-huh --- I guess I must withdraw at this point!   WFL



On 7/24/19, israel at math.ubc.ca <israel at math.ubc.ca> wrote:
> No, q is not a(q-1) in general, just for odd primes. For example, if p =
> 127, the divisors of t_126 less than p are 1 = a(1), 3 = a(2), 7 = a(6), 9
> = a(9), 21 = a(14), 63 = a(62).
>
> Cheers,
> Robert
>
>
>
> On Jul 24 2019, Fred Lunnon wrote:
>
>>  By induction: if q|(p-1) then q = a(q-1) has appeared earlier; the only
>> divisor of t_p remaining is p itself, so a(p-1) = p . QED WFL
>>
>>
>>
>>On 7/24/19, Neil Sloane <njasloane at gmail.com> wrote:
>>> E.N. noticed that in A111273 (definition: a(n) = smallest divisor of
>>> t_n = n(n+1)/2 that has not yet appeared in the sequence), it seems that
>>> a(p-1)=p for all odd primes p. Surely this can't be a hard problem?
>>>
>>> It would follow if we knew that the smallest missing number (smn) in
>>> A111273 (which is now A309195) is always >n/2.
>>>
>>> --
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>
>>--
>>Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>