The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS 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(pr, v=concat(v, q), q=m)); return(v); } CROSSREFS Cf. A003173, A338087. Sequence in context: A154676 A250926 A278200 * A246226 A204944 A184771 Adjacent sequences:  A340052 A340053 A340054 * A340056 A340057 A340058 KEYWORD nonn AUTHOR Marco Frigerio, Dec 29 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 23:04 EDT 2021. Contains 347596 sequences. (Running on oeis4.)