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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 (list; graph; refs; listen; history; text; internal format)
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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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 * A123079 A273950 A268511

Adjacent sequences:  A145013 A145014 A145015 * A145017 A145018 A145019

KEYWORD

nonn,easy

AUTHOR

Vladimir Shevelev, Sep 29 2008

STATUS

approved

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Last modified May 16 22:18 EDT 2021. Contains 343957 sequences. (Running on oeis4.)