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%I #17 Sep 08 2022 08:46:05
%S 1,3,4,7,8,11,12,14,15,16,18,19,22,23,26,27,29,30,33,34,37,38,40,41,
%T 42,44,45,48,49,52,53,55,56,57,59,60,63,64,67,68,70,71,74,75,78,79,82,
%U 83,85,86,89,90,93,94,96,97,98,100,101,104,105,108,109,111,112,113,115,116,119,120,123,124,126
%N Numbers n such that there exists a square m^2 with 3n^2 - n <= m^2 <= 3n^2 + n.
%H Robert Israel, <a href="/A229081/b229081.txt">Table of n, a(n) for n = 1..10000</a>
%e There is a square between 3*4^2-4 and 3*4^2+4 (44<=49<=52) but not between 3*5^2-5=70 and 3*5^2+5=80, so 4 is in sequence but not 5.
%p filter:= n -> ceil(sqrt(3*n^2-n))<=floor(sqrt(3*n^2+n)):
%p select(filter, [$1..200]); # _Robert Israel_, Jan 05 2020
%o (PARI) for(n=1,200,for(i=-n,n,f=0;if(issquare(3*n*n+i),f=1;break));if(f,print1(n,",")))
%o (Magma) [n: n in [1..130] | exists{3*n^2+i: i in [-n..n] | IsSquare(3*n^2+i)}]; // _Bruno Berselli_, Sep 13 2013
%Y Cf. A006451, A072221.
%K nonn
%O 1,2
%A _Ralf Stephan_, Sep 13 2013
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