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The largest k such that an integer x between 1 and k (inclusive) can be guessed in at most n queries "is x < y?" with one lie.
1

%I #10 Oct 07 2019 16:25:36

%S 1,1,1,2,2,4,7,12,22,40,76,142,268,500,944,1788,3389,6444,12286,23464

%N The largest k such that an integer x between 1 and k (inclusive) can be guessed in at most n queries "is x < y?" with one lie.

%D S. M. Ulam, "Adventures of a Mathematician", Scribner’s, 1976.

%H A. Pelc, <a href="https://doi.org/10.1016/0097-3165(87)90065-3">Solution of Ulam’s Problem on searching with a lie</a>, J. Combinatorial Theory, Series A, vol. 44 (1987), 129-140.

%Y Cf. A286496 (with queries about membership of an arbitrary set instead of a set {x < y}).

%K nonn,more

%O 0,4

%A _Mikhail Tikhomirov_, Sep 08 2019