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

1,3

Comments

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

Links

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

Example

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.

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

Crossrefs

Cf. A224853, A003278, A005836, A000452.

Sequence in context: A191192 A139063 A224853 * A191134 A196101 A200816

Adjacent sequences: A225568 A225569 A225570 * A225572 A225573 A225574

Keyword

nonn,look

Author

Giovanni Resta, Jul 29 2013

Status

approved