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

11, 60, 63, 84, 112, 180, 189, 252, 275, 660, 693, 924, 1232, 1326, 1768, 1974, 2632, 4026, 5368, 6405, 8200, 8319, 11092, 11715, 15620, 16401, 19720, 20706, 20880, 20910, 24752, 24960, 25300, 26565, 29716, 29835, 33048, 35055, 41496, 42997

Offset: 1

Author

Zak Seidov, Oct 25 2002

Keywords

• nonn

Comments

The sequence is infinite.

Links

• Robert Israel, Table of n, a(n) for n = 1..986

Crossrefs

Cf. A076600.

Programs

Maple

A076600:= proc(n) local q;
  q:= max(select(t -> n^2/t - t > 2*n and (t - n^2/t)::even, numtheory:-divisors(n^2)));
  if q = -infinity then 0 else (n^2/q - q)/2 fi;
end proc:
A[1]:= 11;
for n from 2 to 100 do
  A[n]:= A076600(A[n-1]);
od:
seq(A[i],i=1..100); # Robert Israel, Mar 22 2018

Mathematica

nmax = 100;
A076600[n_] := Module[{q},
  q = Max[Select[Divisors[n^2], n^2/# - # > 2n &&
  EvenQ[# - n^2/#]&]];
  If[q == -Infinity, 0, (n^2/q - q)/2]];
a[1] = 11;
For[n = 2, n <= nmax, n++, a[n] = A076600[a[n - 1]]];
Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, May 17 2023, after Robert Israel *)