A sequence based on consecutive primes

[Don Reble]

>   a = sqrt((p^2 + q^2)/2 - 1).   (1)
> 
> ...the smallest prime q > p + 2 which makes a an integer, ...
> 0 is used if there is no such q:
>
> 11, 263, 59, 23, 101, 109, 0, 151, 193, 79, 269, 277, 311, 0, 179, 83,
> 83003, 479, 487, 181, 563, 571, 613, 1201, 157, 141509, 739, 773, 479
>
> ... There is no such q for p = 19 and p = 47
> (consider (1) modulo 7), but I can find no similar proof of
> impossibility for p = 127, which would generate the next term in the
> above sequence.

    I get p=19,q=1278886952463697; p=127,q=6858037981;
    but I find no q for p=47.
    Even though I distrust the modulo-7 proof, how does it go?

-- 
Don Reble  djr at nk.ca


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