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 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 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(pr, v=concat(v, q), q=m)); return(v); } CROSSREFS Cf. A000926, A338088. Sequence in context: A236449 A352110 A253467 * A340405 A258704 A224592 Adjacent sequences: A340129 A340130 A340131 * A340133 A340134 A340135 KEYWORD nonn AUTHOR Marco Frigerio, Dec 29 2020 STATUS approved

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Last modified March 20 22:57 EDT 2023. Contains 361392 sequences. (Running on oeis4.)