A087879 Primes of the form (4n+1)^2 + (4m+2)^2, m,n >= 0.

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

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