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%I #17 Jan 10 2020 05:24:51
%S 0,3,12,27,36,48,63,75,108,111,147,156,171,192,228,243,291,300,324,
%T 336,363,372,387,399,432,468,507,576,588,603,624,651,675,687,723,732,
%U 756,768,831,867,876,948,972,975,1008,1083,1092,1116,1200,1227,1236,1251,1263,1296,1299,1323,1332,1371
%N Löschian numbers (A003136) k such that k + 1 is also Löschian number.
%C May be called lesser of twin Löschian pairs.
%H Amiram Eldar, <a href="/A271183/b271183.txt">Table of n, a(n) for n = 1..10000</a>
%e 3 is a term because 3 = 1^2 + 1*1 + 1^2 and 3 + 1 = 4 = 0^2 + 0*2 + 2^2.
%t Select[Range[0, 1400], AllTrue[{#, # + 1}, Resolve[Exists[{x, y}, Reduce[# == x^2 + x y + y^2, {x, y}, Integers]]] &] &] (* Version 10, or *)
%t Select[Range[0, 1400], Times @@ Boole@ Map[Resolve[Exists[{x, y}, Reduce[# == x^2 + x y + y^2, {x, y}, Integers]]] &, {#, # + 1}] == 1 &] (* _Michael De Vlieger_, Apr 01 2016 *)
%o (PARI) has(n) = #bnfisintnorm(bnfinit(z^2+z+1), n);
%o print1(0,", "); for(n=1, 2000, if(has(n) && has(n+1), print1(n,", ")));
%Y Cf. A003136.
%K nonn
%O 1,2
%A _Altug Alkan_, Apr 01 2016
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