A351027 a(n) is the least number that starts a sequence of exactly n nonsquarefree numbers under the iteration x_{n+1} = x_n^2 - x_n + 1.

4, 68, 1832, 80796

Offset

1,1

Comments

1000000 < a(5) <= 58229352.

Links

Table of n, a(n) for n=1..4.

Example

a(3) = 1832 because 1832 is divisible by 2^2, 1832^2-1832+1 = 3354393 is divisible by 7^2, 3354393^2-3354393+1 = 11251949044057 is divisible by 97^2, and 11251949044057^2-11251949044057+1 = 126606357290043984177975193 is squarefree, and 1832 is the smallest number that works.

Maple

f:= proc(n) local x, i;
x:= n;
for i from 0 do
  if numtheory:-issqrfree(x) then return count fi;
  x:= x^2-x+1
od
end proc:
W:= Vector(4):
for n from 1 while W[4] = 0 do
  v:= f(n);
  if v >= 1 and W[v] = 0 then W[v]:= n fi
od:
convert(W, list);

Crossrefs

Cf. A013929.

Sequence in context: A156084 A362730 A000658 * A156470 A326288 A302115

Adjacent sequences: A351024 A351025 A351026 * A351028 A351029 A351030

Keyword

nonn,more

Author

Robert Israel, Feb 03 2022

Status

approved