[seqfan] Re: Question from Harvey Dale about A233552

[israel at math.ubc.ca]

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.
Cheers,
Robert

On May 26 2019, 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.
>
>Cheers,
>Robert
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>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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>>
>>
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