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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.
0
4, 68, 1832, 80796
OFFSET
1,1
COMMENTS
1000000 < a(5) <= 58229352.
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
KEYWORD
nonn,more
AUTHOR
Robert Israel, Feb 03 2022
STATUS
approved