A199854 - OEIS

%I #16 Aug 02 2019 21:15:27

%S 3,11,59,83,107,131,179,227,251,347,443,467,563,587,971,1019,1091,

%T 1187,1259,1283,1307,1451,1523,1571,1619,1811,1907,1931,2027,2099,

%U 2411,2459,2579,2819,2939,2963,3203,3251,3299,3371,3467,3491,3539,3779,3803,3923,3947

%N Primes of the form 1 + m^2 + n^2 with gcd(m,n)=1.

%H J. Wu, <a href="http://dx.doi.org/10.1090/S0002-9939-98-04414-1 ">Primes of the form 1 + m^2 + n^2 in short intervals</a>, Proc. Amer. Math. Soc. 126 (1998), 1-8

%e First such decompositions are 3 = 1 + 1^2 + 1^2, 11 = 1 + 1^2 + 3^2, 59 = 1 + 3^2 + 7^2.

%e First instance of several decompositions for the same prime: 131 = 1 + 3^2 + 11^2 = 1 + 7^2 + 9^2.

%o (PARI) hasform(p) = {q = p - 1; for (k = 1, q/2, if (issquare(k) && issquare(q-k) && (gcd(k, q-k)==1), return(1));); return(0);}

%Y Cf. A056899 (when the decomposition has m=1).

%K nonn

%O 1,1

%A _Michel Marcus_, Dec 22 2012