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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.
2
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
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
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Apr 02 2002
EXTENSIONS
Offset corrected by Robert Israel, Jun 29 2018
STATUS
approved