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

[israel at math.ubc.ca]

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.
>>
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