A316741 Numbers k with the property that there exists a matrix of squares m = [p^2, q^2; r^2, s^2] such that p, q, r, s are all distinct primes less than k, and det(m) = k.

29, 43, 67, 69, 77, 115, 136, 171, 173, 187, 189, 219, 224, 235, 237, 245, 259, 267, 283, 285, 291, 296, 317, 339, 341, 344, 355, 365, 368, 376, 381, 403, 405, 411, 413, 424, 427, 429, 435, 437, 451, 453, 485, 501, 507, 536, 549, 555, 568, 576, 595, 597, 603, 605

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Example

29 belongs to this sequence because we have a matrix m = [25, 49; 4, 9] in which each element is the square of a prime smaller than 29, and det(m) = 25*9 - 49*4 = 29.

Mathematica

t[x_, n_] := Block[{f = FactorInteger@x}, Last /@ f == {1, 1} && f[[2, 1]] < n]; ok[n_] := Block[{s = List@ ToRules@ Reduce[n == x^2-y^2 && x>y>0, {x, y}, Integers]}, s =!= {} && AnyTrue[ {x, y}/.s, GCD @@ # == 1 && t[#[[1]], n] && t[#[[2]], n] &]]; Select[Range[400], ok] (* Giovanni Resta, Jul 12 2018 *)

Prog

(MiniZinc)
include "globals.mzn";
int: n = 4;
%to get all numbers less than 250 of this sequence
int: max_val = 250;
array[1..n+1] of var 2..max_val: x;
% primes between 2..max_val
set of int: prime = 2..max_val diff { i | i in 2..max_val, j in 2..ceil(sqrt(i)) where i mod j = 0} ;
set of int: primes;
primes = prime union {2};
solve satisfy;
constraint all_different(x) /\ x[1] in primes /\ x[2] in primes /\ x[3] in primes /\ x[4] in primes /\ forall(i in 1..n) ((x[i]<x[5])) /\ pow(x[1], 2)*pow(x[4], 2)-pow(x[2], 2)*pow(x[3], 2) = x[5];
output [ show(x[5]) ];

Crossrefs

Sequence in context: A341666 A247896 A162357 * A173967 A004619 A140444

Adjacent sequences: A316738 A316739 A316740 * A316742 A316743 A316744

Keyword

nonn

Author

Pierandrea Formusa, Jul 11 2018

Extensions

More terms from Giovanni Resta, Jul 12 2018

Status

approved