A069018 Smallest square k > 0 such that n*k + 1 is also a square or 0 if no such term exists, i.e., when n is a square.

0, 4, 1, 0, 16, 4, 9, 1, 0, 36, 9, 4, 32400, 16, 1, 0, 64, 16, 1521, 4, 144, 1764, 25, 1, 0, 100, 25, 576, 3312400, 4, 74529, 9, 16, 36, 1, 0, 144, 36, 16, 9, 102400, 4, 281961, 900, 576, 12873744, 49, 1, 0, 196, 49, 8100, 82810000, 4356, 144, 4, 400, 6625476

Offset

1,2

Comments

Terms from Robert G. Wilson v.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

f:= proc(n) local x, y, t, z, k, r;
  if issqr(n) then return 0 fi;
  t:= [isolve(n*x^2+1=y^2)];
  z:= (indets(t, name) minus {x, y})[1];
  for k from 0 do
    r:= select(`>`, map(s -> eval(x, s), eval(t, z=k)), 0);
    if nops(r) >= 1 then return min(r)^2 fi
  od
end proc:
map(f, [$1..100]); # Robert Israel, Jun 29 2018

Mathematica

Do[k = 0; If[ !IntegerQ[ Sqrt[n]], k = 1; While[ !IntegerQ[ Sqrt[n*k^2 + 1]], k++ ]]; Print[k^2], {n, 1, 35}] (* Robert G. Wilson v *)

Crossrefs

Sequence in context: A007789 A345393 A081114 * A156811 A246609 A371080

Adjacent sequences: A069015 A069016 A069017 * A069019 A069020 A069021

Keyword

nonn

Author

Amarnath Murthy, Apr 02 2002

Extensions

Offset corrected by Robert Israel, Jun 29 2018

Status

approved