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A087879 Primes of the form (4n+1)^2 + (4m+2)^2, m,n >= 0. 1
5, 29, 37, 61, 101, 173, 181, 197, 269, 277, 293, 349, 389, 509, 541, 613, 653, 661, 677, 701, 757, 773, 821, 877, 941, 1069, 1093, 1109, 1117, 1181, 1237, 1301, 1373, 1597, 1613, 1693, 1733, 1741, 1789, 1877, 1933, 1997, 2029, 2053, 2069, 2141, 2221, 2269 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

N:= 10000:

A:= NULL:

for x from 1 by 4 while x^2 < N do

  for y from 2 by 4 while x^2 + y^2 < N do

    v:= x^2 + y^2;

    if isprime(v) then A:= A, v fi

od od:

sort(convert({A}, list)); # Robert Israel, Aug 26 2018

PROG

Contribution from Michael B. Porter, Dec 10 2009: (Start)

(PARI) /* numbers of the form (4x+1)^2 + (4y+2)^2 for x, y >= 0 */

/* largest possible x */

xm(n)=floor((sqrt(n-4)-1)/4)

/* determine if n - (4x+1)^2 is a square, and put the square root into a */

isform(n)={local(r, a); r=0; for(x=0, xm(n), if(issquare(n-(4*x+1)^2, a), if(Mod(a, 4)==Mod(2, 4), r=1))); r}

/* skip isform() calculation if possible */

isA087879(n) = if(n>4 && Mod(n, 2)==Mod(1, 2) && isprime(n), isform(n), 0) (End)

CROSSREFS

Sequence in context: A115279 A279393 A182288 * A091729 A033205 A167742

Adjacent sequences:  A087876 A087877 A087878 * A087880 A087881 A087882

KEYWORD

nonn

AUTHOR

Cino Hilliard, Oct 11 2003

STATUS

approved

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Last modified July 19 12:35 EDT 2019. Contains 325159 sequences. (Running on oeis4.)