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A373328 Numbers k such that the difference between T = k*(k+1)/2 = A000217(k) and the largest square <= T reaches a new record.

%I A373328 #11 Dec 19 2024 23:40:25
%S A373328 0,2,5,9,12,15,19,22,29,32,39,46,53,56,63,70,73,80,87,90,97,104,111,
%T A373328 114,121,131,155,172,189,213,230,254,271,295,312,329,353,370,394,411,
%U A373328 428,452,469,493,510,527,551,568,592,609,633,650,667,691,708,732,749,766
%N A373328 Numbers k such that the difference between T = k*(k+1)/2 = A000217(k) and the largest square <= T reaches a new record.
%H A373328 Robert Israel, <a href="/A373328/b373328.txt">Table of n, a(n) for n = 1..10000</a>
%p A373328 J:= 0: m:= 0: count:= 1:
%p A373328 for i from 1 while count < 100 do
%p A373328   t:= i*(i+1)/2;
%p A373328   v:= t - floor(sqrt(t))^2;
%p A373328   if v > m then
%p A373328     J:= J,i; m:= v; count:= count+1;
%p A373328    fi
%p A373328 od:
%p A373328 J; # _Robert Israel_, Dec 19 2024
%o A373328 (PARI) a373328(nmax) = {my(m=-oo); for(n=0, nmax, my(T=n*(n+1)/2, d=T-sqrtint(T)^2); if(d>m, print1(n, ", "); m=d))};
%o A373328 a373328(770)
%Y A373328 A373327 gives the corresponding differences.
%Y A373328 Cf. A000217, A000290, A064784, A128549.
%K A373328 nonn
%O A373328 1,2
%A A373328 _Hugo Pfoertner_, Jun 01 2024