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

 

Logo


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

Table of n, a(n) for n=1..26.

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

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.

License Agreements, Terms of Use, Privacy Policy. .

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