A085902 a(0) = 2, a(n) is the smallest squarefree number > a(n-1) such that the sum a(n) + a(i) for all i = 1 to (n-1) is squarefree. Or, sum of any two terms is a squarefree number.

2, 3, 11, 19, 55, 59, 83, 111, 127, 155, 163, 199, 203, 219, 263, 299, 307, 311, 371, 383, 399, 455, 515, 803, 883, 919, 983, 1063, 1499, 1559, 1927, 2019, 2063, 2183, 2215, 2271, 2359, 2503, 2703, 2755, 2999, 3459, 3899, 3927, 4271, 4303, 4411, 4519, 4559

Offset: 0

Author

Amarnath Murthy, Jul 09 2003

Keywords

• nonn

Comments

It can easily be proved that a(n) == 3 (mod 4) for all n > 2.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A005117, A077224, A077225, A080793.

Programs

Mathematica

a[0] = 2; a[n_] := a[n] = Module[{t = Array[a, n, 0], k = a[n - 1] + 1}, While[! SquareFreeQ[k] || AnyTrue[t, ! SquareFreeQ[k + #] &], k++]; k]; Array[a, 100, 0] (* Amiram Eldar, Aug 21 2023 *)

Extensions

More terms from Ray Chandler, Sep 13 2003