S000159


Nonnegative numbers n for which n^2 - n + 41 is not squarefree.

41, 604, 799, 891, 918, 1246, 1254, 1319, 1641, 1652, 1722, 2011, 2070, 2252, 2453, 2607, 2650, 3095, 3100, 3322, 3403, 3528, 3608, 4124, 4240, 4302, 4820, 4944, 5003, 5084, 5309, 5373, 5426, 5737, 5791, 5931, 5959, 5999, 6151, 6417, 6512, 6684, 6765

1

S000159

This quadratic is prime for n = 0..40. If we look at the differences of these numbers, it is clear that 81 is a common difference. Why? This is shown in S000162. The discriminant of this quadratic is 163, which is 2*81 + 1.

T. D. Noe, Plot of 1000 terms

T. D. Noe, Table of 1000 terms

Wikipedia, Formula for primes

(Mma) Select[Range[0, 10000], ! SquareFreeQ[#^2 - # + 41] &]

Cf. A202018 (n^2 + n + 41), S000160, S000161, S000162.

nonn

T. D. Noe, Jul 22 2014

© Tony D Noe 2014-2015