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The integer k that minimizes |k/2^n - log 2|.
3

%I #4 Oct 11 2017 18:14:32

%S 1,1,3,6,11,22,44,89,177,355,710,1420,2839,5678,11357,22713,45426,

%T 90852,181704,363409,726817,1453635,2907270,5814540,11629080,23258160,

%U 46516320,93032640,186065279,372130559,744261118,1488522236,2977044472,5954088944

%N The integer k that minimizes |k/2^n - log 2|.

%H Clark Kimberling, <a href="/A293364/b293364.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = floor(1/2 + (log 2)*2^n).

%F a(n) = A293362(n) if (fractional part of (log 2)*2^n) < 1/2, else a(n) = A293363(n).

%t z = 120; r = Log[2];

%t Table[Floor[r*2^n], {n, 0, z}]; (* A293362 *)

%t Table[Ceiling[r*2^n], {n, 0, z}]; (* A293363 *)

%t Table[Round[r*2^n], {n, 0, z}]; (* A293364 *)

%Y Cf. A002162, A293362, A293363.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Oct 11 2017