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Select[Partition[Prime[Range[4000]], 2, 1], OddQ[Sqrt[1+4*Mean[#]]]&][[All, 1]] (* Harvey P. Dale, Oct 25 2020 *)
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f[n_] := NextPrime[n*(n + 1), -1] ; f /@ Select[Range[200], (ob = #*(# + 1)) == (NextPrime[ob, -1] + NextPrime[ob])/2 &] (* Amiram Eldar, May 06 2020 *)
Amiram Eldar, <a href="/A242383/b242383.txt">Table of n, a(n) for n = 1..10000</a>
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