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A145016
Primes p of the form 4k+1 for which p - floor(sqrt(p))^2 is a square.
19
5, 13, 17, 29, 37, 53, 73, 97, 101, 109, 137, 173, 197, 229, 241, 257, 281, 293, 349, 397, 401, 409, 457, 509, 577, 601, 641, 661, 677, 701, 733, 809, 857, 877, 977, 997, 1033, 1049, 1093, 1153, 1181, 1229, 1289, 1297, 1321, 1373, 1433, 1453, 1493, 1601, 1609
OFFSET
1,1
COMMENTS
If a(n) = x^2 + y^2 then y = floor(sqrt(a(n))) and by a well known Euler theorem, the representation is unique.
Odd primes p = x^2 + y^2 such that y > x^2/2. - Thomas Ordowski, Aug 16 2014
LINKS
MAPLE
filter:= p -> isprime(p) and issqr(p - floor(sqrt(p))^2):
select(filter, [seq(p, p=1..10000, 4)]); # Robert Israel, Dec 04 2018
MATHEMATICA
okQ[n_]:=PrimeQ[n]&&IntegerQ[Sqrt[n-Floor[Sqrt[n]]^2]]; Select[4Range[500]+1, okQ] (* Harvey P. Dale, Mar 23 2011 *)
PROG
(PARI) isok(p) = isprime(p) && ((p%4) == 1) && issquare(p - sqrtint(p)^2); \\ Michel Marcus, Dec 04 2018
CROSSREFS
Subsequence of A002144 (Pythagorean primes).
Sequence in context: A111055 A307096 A283391 * A372078 A354155 A123079
KEYWORD
nonn,easy
AUTHOR
Vladimir Shevelev, Sep 29 2008
STATUS
approved