A077224 a(0) = 1; for n > 1, a(n) = smallest number > a(n-1) such that a(n) + a(k) is squarefree for k = 1 to n-1.

1, 2, 4, 9, 13, 29, 33, 101, 105, 109, 157, 177, 253, 289, 301, 353, 409, 429, 465, 501, 533, 553, 589, 609, 681, 753, 877, 933, 965, 1153, 1477, 1905, 1977, 2101, 2125, 2229, 2305, 2405, 2605, 2657, 2801, 2913, 3305, 3381, 3489, 3565, 3777, 3781, 3881, 4029

Offset: 0

Author

Amarnath Murthy, Nov 03 2002

Keywords

• nonn

Comments

Or, sum of any two terms is a squarefree number.

Examples

			13 is a member as 13 + 1, 13 + 2, 13 + 4, 13 + 9 are all squarefree.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..1800

Crossrefs

Cf. A005117, A077225, A080793, A085902.

Programs

Mathematica

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

Formula

It can easily be proved that a(n) == 1 mod 4 for all n > 3.

Extensions

Edited by Sam Alexander, Dec 12 2003