A076676 - OEIS

%I #10 May 17 2023 10:51:35

%S 11,60,63,84,112,180,189,252,275,660,693,924,1232,1326,1768,1974,2632,

%T 4026,5368,6405,8200,8319,11092,11715,15620,16401,19720,20706,20880,

%U 20910,24752,24960,25300,26565,29716,29835,33048,35055,41496,42997

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

%C The sequence is infinite.

%H Robert Israel, <a href="/A076676/b076676.txt">Table of n, a(n) for n = 1..986</a>

%p A076600:= proc(n) local q;

%p   q:= max(select(t -> n^2/t - t > 2*n and (t - n^2/t)::even, numtheory:-divisors(n^2)));

%p   if q = -infinity then 0 else (n^2/q - q)/2 fi;

%p end proc:

%p A[1]:= 11;

%p for n from 2 to 100 do

%p   A[n]:= A076600(A[n-1]);

%p od:

%p seq(A[i],i=1..100); # _Robert Israel_, Mar 22 2018

%t nmax = 100;

%t A076600[n_] := Module[{q},

%t   q = Max[Select[Divisors[n^2], n^2/# - # > 2n &&

%t   EvenQ[# - n^2/#]&]];

%t   If[q == -Infinity, 0, (n^2/q - q)/2]];

%t a[1] = 11;

%t For[n = 2, n <= nmax, n++, a[n] = A076600[a[n - 1]]];

%t Table[a[n], {n, 1, nmax}] (* _Jean-François Alcover_, May 17 2023, after _Robert Israel_ *)

%Y Cf. A076600.

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 25 2002