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%I #17 Sep 08 2022 08:45:52
%S 5,17,53,137,173,257,677,1097,1193,1733,2237,2657,2957,4133,5297,5717,
%T 8573,8837,9377,11093,11393,12953,14957,17477,18233,18617,19793,23537,
%U 24413,29033,30497,33533,36713,40037,41177,45293,48353
%N Primes of the form 5*x^2 - 3*y^2, where x and y are consecutive numbers.
%C a(n) is congruent to 1 (mod 4).
%C Primes of the form 2*k^2 + 10*k + 5 or 2*k^2 - 6*k - 3. - _Vincenzo Librandi_, Apr 19 2010
%H Harvey P. Dale, <a href="/A176470/b176470.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[Table[5n^2-3(n+1)^2,{n,4,200}],PrimeQ] (* _Harvey P. Dale_, Aug 07 2017 *)
%o (Magma) [ p: p in PrimesUpTo(60000) | exists(t){ n: n in [1..Isqrt(p)] | p eq 5*n^2-3*(n-1)^2 } ]; //y = x-1
%K nonn
%O 1,1
%A _Giovanni Teofilatto_, Apr 18 2010
%E Comment corrected by _Giovanni Teofilatto_, Apr 19 2010
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