|
%I #19 Dec 04 2018 11:02:54
%S 5,13,17,29,37,53,73,97,101,109,137,173,197,229,241,257,281,293,349,
%T 397,401,409,457,509,577,601,641,661,677,701,733,809,857,877,977,997,
%U 1033,1049,1093,1153,1181,1229,1289,1297,1321,1373,1433,1453,1493,1601,1609
%N Primes p of the form 4k+1 for which p - floor(sqrt(p))^2 is a square.
%C If a(n) = x^2 + y^2 then y = floor(sqrt(a(n))) and by a well known Euler theorem, the representation is unique.
%C Odd primes p = x^2 + y^2 such that y > x^2/2. - _Thomas Ordowski_, Aug 16 2014
%H Vincenzo Librandi, <a href="/A145016/b145016.txt">Table of n, a(n) for n = 1..1000</a>
%p filter:= p -> isprime(p) and issqr(p - floor(sqrt(p))^2):
%p select(filter, [seq(p,p=1..10000,4)]); # _Robert Israel_, Dec 04 2018
%t okQ[n_]:=PrimeQ[n]&&IntegerQ[Sqrt[n-Floor[Sqrt[n]]^2]]; Select[4Range[500]+1,okQ] (* _Harvey P. Dale_, Mar 23 2011 *)
%o (PARI) isok(p) = isprime(p) && ((p%4) == 1) && issquare(p - sqrtint(p)^2); \\ _Michel Marcus_, Dec 04 2018
%Y Subsequence of A002144 (Pythagorean primes).
%K nonn,easy
%O 1,1
%A _Vladimir Shevelev_, Sep 29 2008
|
