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!)
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). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

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

EXAMPLE

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.

PROG

(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(p<m, p=nextprime(p+1); if(isok(p, u), return(p))); return(0)}

Lista(m)={ my (q, r=108*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. A000926, A338088.

Sequence in context: A252038 A236449 A253467 * A340405 A258704 A224592

Adjacent sequences:  A340129 A340130 A340131 * A340133 A340134 A340135

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 21 16:31 EDT 2021. Contains 347598 sequences. (Running on oeis4.)