A340132 Least prime numbers, in ascending order, such that each of them can be written, in a unique way, in the form x^2 + h*y^2, where x, y are natural numbers, while h takes all the values of the sequence A000926 (idoneal numbers).

1083289, 3818929, 6104641, 6868801, 7623529, 8465209, 9033649, 10105489, 11400481, 11597569, 11809561, 12338041, 12348961, 13154761, 13426009, 15861169, 16889161, 16922161, 18596449, 19684729, 20322481, 21067201, 21480001, 22684561, 23654569, 24531049

Offset: 1

Author

Marco Frigerio, Dec 29 2020

Keywords

• nonn

Comments

First number in this sequence is equal to last number of sequence A338088.

The sequence is obtained using Lista(m), with m=246*10^5, see section PROG. It's possible to increase m to discover more terms of the sequence.

Examples

			1083289 =  315^2  + A000926(1)*992^2
        = 1033^2  + A000926(2)*90^2
        =  979^2  + A000926(3)*204^2
        = ...
        =  817^2  + A000926(65)*15^2.
		

Crossrefs

Cf. A000926, A338088.

Programs

PARI

Idoneal()={return(select(m->!#select(k->k<>2, quadclassunit(-4*m).cyc), [1..1848]));}
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=Idoneal()); while(pr,v=concat(v,q),q=m)); return(v);}