

A225571


Lexicographically earliest sequence of nonnegative integers which does not contain a threeterm arithmetic or geometric subsequence.


3



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
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OFFSET

1,3


COMMENTS

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


LINKS



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



KEYWORD



AUTHOR



STATUS

approved



