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

0,1

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

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 *)

Crossrefs

Cf. A005117, A077224, A077225, A080793.

Sequence in context: A051101 A045339 A051091 * A051083 A051097 A214773

Adjacent sequences: A085899 A085900 A085901 * A085903 A085904 A085905

Keyword

nonn

Author

Amarnath Murthy, Jul 09 2003

Extensions

More terms from Ray Chandler, Sep 13 2003

Status

approved