[seqfan] Re: Question from Harvey Dale about A233552

[israel at math.ubc.ca]

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





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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