A340055 Primes that can be written in the form j^2 + h*k^2, where j and k are positive integers, for every h in A003173 (Heegner numbers).

2333017, 5995081, 11414209, 11941273, 12953593, 14823769, 18550849, 19231969, 23582161, 26603977, 27336457, 29236729, 32630161, 35452033, 35836249, 37895089, 40411177, 42911257, 46007329, 46087057, 49680577, 49825609, 52046593, 52208017, 55624297, 63257401

Offset: 1

Author

Marco Frigerio, Dec 29 2020

Keywords

• nonn

Comments

The first term in this sequence is equal to last term in A338087.

The sequence is obtained using Lista(m), with m=633*10^5, see section PROG. One can increase m to obtain further terms of the sequence.

Examples

			2333017 =  989^2 + A003173(1)*1164^2
        = 1493^2 + A003173(2)*228^2
        = 1093^2 + A003173(3)*616^2
        =  685^2 + A003173(4)*516^2
        = 1349^2 + A003173(5)*216^2
        =  179^2 + A003173(6)*348^2
        = 1293^2 + A003173(7)*124^2
        = 1395^2 + A003173(8)*76^2
        = 1485^2 + A003173(9)*28^2.
		

Crossrefs

Cf. A003173, A338087.

Programs

PARI

Heegner()={my (d, k, v);  v=vector(3, i, i); for(k=2, 41, d=4*k-1; if(isprime(d) && qfbclassno(-d)==1, v=concat(v, d))); return(v);}
isok(p,u)={my (i, s, n=matsize(u)[2], t=0);for(i=1, n, s=kronecker(-u[i],p); if(s==1, t++,break));if(t==n,t=0;for(i=1, n, s=qfbsolve(Qfb(1,0,u[i]),p); if(s==[], break,t++)));if(t==n,1,0)}
Primo(p, m)={my(u=Heegner()); while(pr,v=concat(v,q),q=m)); return(v);}