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A076676 Smallest a(n)>a(n-1) such that a(n)^2+a(n-1)^2 is a perfect square, a(1)=11.

%I A076676 #10 May 17 2023 10:51:35
%S A076676 11,60,63,84,112,180,189,252,275,660,693,924,1232,1326,1768,1974,2632,
%T A076676 4026,5368,6405,8200,8319,11092,11715,15620,16401,19720,20706,20880,
%U A076676 20910,24752,24960,25300,26565,29716,29835,33048,35055,41496,42997
%N A076676 Smallest a(n)>a(n-1) such that a(n)^2+a(n-1)^2 is a perfect square, a(1)=11.
%C A076676 The sequence is infinite.
%H A076676 Robert Israel, <a href="/A076676/b076676.txt">Table of n, a(n) for n = 1..986</a>
%p A076676 A076600:= proc(n) local q;
%p A076676   q:= max(select(t -> n^2/t - t > 2*n and (t - n^2/t)::even, numtheory:-divisors(n^2)));
%p A076676   if q = -infinity then 0 else (n^2/q - q)/2 fi;
%p A076676 end proc:
%p A076676 A[1]:= 11;
%p A076676 for n from 2 to 100 do
%p A076676   A[n]:= A076600(A[n-1]);
%p A076676 od:
%p A076676 seq(A[i],i=1..100); # _Robert Israel_, Mar 22 2018
%t A076676 nmax = 100;
%t A076676 A076600[n_] := Module[{q},
%t A076676   q = Max[Select[Divisors[n^2], n^2/# - # > 2n &&
%t A076676   EvenQ[# - n^2/#]&]];
%t A076676   If[q == -Infinity, 0, (n^2/q - q)/2]];
%t A076676 a[1] = 11;
%t A076676 For[n = 2, n <= nmax, n++, a[n] = A076600[a[n - 1]]];
%t A076676 Table[a[n], {n, 1, nmax}] (* _Jean-François Alcover_, May 17 2023, after _Robert Israel_ *)
%Y A076676 Cf. A076600.
%K A076676 nonn
%O A076676 1,1
%A A076676 _Zak Seidov_, Oct 25 2002