A225571 Lexicographically earliest sequence of nonnegative integers which does not contain a three-term arithmetic or geometric subsequence.

0, 1, 3, 4, 10, 11, 13, 14, 29, 30, 32, 33, 38, 39, 41, 42, 85, 86, 88, 89, 94, 95, 97, 98, 112, 113, 115, 116, 122, 123, 125, 238, 248, 251, 252, 255, 257, 260, 261, 273, 275, 278, 279, 287, 288, 292, 330, 331, 334, 335

Offset: 1

Author

Giovanni Resta, Jul 29 2013

Keywords

• nonn
• look

Comments

This sequence diverges from A224853 at 477th term. Here a(477) = 17380, while A224853(477) = 17408.

Examples

			After terms 0, 1, 3, 4 have been added, the terms 5,...,9 are forbidden by subsequences (3,4,5), (0,3,6), (1,4,7), (0,4,8) and (1,3,9) so the next term is 10.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A224853, A003278, A005836, A000452.

Programs

Mathematica

seq = {0, 1}; bad[n_] := Catch[ Do[If[MemberQ[seq, (n + e)/2], Throw@True], {e, seq}];  Do[If[MemberQ[seq, Sqrt[n*e]], Throw@True], {e, Rest@ seq}]; False]; While[Length[seq] < 100, x = Last[seq]+1; While[bad[x], x++]; AppendTo[seq, x]]; seq