[seqfan] Re: Question from Harvey Dale about A233552
Harvey P. Dale
hpd at hpdale.org
Mon May 27 04:33:05 CEST 2019
Of the many helpful responses, Robert's is particularly helpful. He finds, for example, that k=6615 shows that 751 is not a term. If there is no top limit to k, how can we be sure than ANY of the suggested terms for the sequence is correct?
From: SeqFan <seqfan-bounces at list.seqfan.eu> On Behalf Of israel at math.ubc.ca
Sent: Sunday, May 26, 2019 8:08 PM
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Question from Harvey Dale about A233552
On the other hand 373 should not be there, as (373*4^2508-1)/3 is prime.
Nor 499, as (499*4^648-1)/3 is prime.
Nor 613, as (613*4^214-1)/3 is prime.
Nor 751, as (751*4^6615-1)/3 is prime.
On May 26 2019, mailto:israel at math.ubc.ca wrote:
>Note that if n=m^2 is a square, n*4^k-1 = (m*2^k-1)*(m*2^k+1), so (if
>m*2^k-1 > 3) (n*4^k-1)/3 must be composite. Thus 25, 49, 121, 169, 289,
>373, 529, 625, 751, 841, 961 should certainly be in the sequence.
>On May 26 2019, Neil Sloane wrote:
>>Harvey just asked me the following question. Can anyone help?
>>I may be missing something, but there seem to be many terms missing
>>from the above sequence. My calculations show that, up to 1000, each
>>of 25, 49, 121, 169, 289, 361, 373, 499, 529, 613, 625, 751, 841, 919,
>>and 961 satisfies the definition, but only 361 and 919 appear in the
>>data. Am I overlooking something? Also, I'm not sure how to test "all
>>k >=1" because that would require going up to infinity - so, is there
>>some top limit to the value of k that should be tested, e.g., k<=n? Or
>>is there some other way to do the test that doesn't require generating lots of terms?
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