OFFSET
1,2
COMMENTS
Dimitrov (2023) proved that this sequence is infinite and gave the formula for its asymptotic density.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Stoyan Dimitrov, Square-free pairs n^2 + n + 1, n^2 + n + 2, HAL preprint, hal-03735444, 2023; ResearchGate link.
EXAMPLE
0 is a term since 0^2 + 0 + 1 = 1 and 0^2 + 0 + 2 = 2 are both squarefree numbers.
MATHEMATICA
Select[Range[0, 150], And @@ SquareFreeQ /@ (#^2 + # + {1, 2}) &]
PROG
(PARI) is(k) = {my(m = k^2 + k + 1); issquarefree(m) && issquarefree(m + 1); }
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Dec 11 2023
STATUS
approved