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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).
1
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
1,1
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.
EXAMPLE
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.
PROG
(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(p<m, p=nextprime(p+1); if(isok(p, u), return(p))); return(0)}
Lista(m)={my (q, r=233*10^4, v=[]); q=nextprime(r); m=precprime(m); while(q<m, r=q; q=Primo(r, m); if(q>r, v=concat(v, q), q=m)); return(v); }
CROSSREFS
Sequence in context: A154676 A250926 A278200 * A246226 A204944 A184771
KEYWORD
nonn
AUTHOR
Marco Frigerio, Dec 29 2020
STATUS
approved