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%I #9 Sep 08 2022 08:46:19
%S 1,1,2,5,9,18,37,74,148,296,591,1182,2364,4729,9457,18914,37828,75657,
%T 151314,302627,605254,1210509,2421018,4842036,9684072,19368144,
%U 38736288,77472575,154945150,309890300,619780601,1239561202,2479122403,4958244807,9916489614
%N The integer k that minimizes |k/2^n - r|, where r = Euler's constant (0.577216...).
%H Clark Kimberling, <a href="/A293354/b293354.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = floor(1/2 + r*2^n), where r = Euler's constant (0.577216...).
%F a(n) = A293352(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293353(n).
%t z = 120; r = EulerGamma;
%t Table[Floor[r*2^n], {n, 0, z}]; (* A293352 *)
%t Table[Ceiling[r*2^n], {n, 0, z}]; (* A293353 *)
%t Table[Round[r*2^n], {n, 0, z}]; (* A293354 *)
%o (PARI) for(n=0,50, print1(round(Euler*2^n), ", ")) \\ _G. C. Greubel_, Aug 29 2018
%o (Magma) R:= RealField(100); [Round(EulerGamma(R)*2^n) : n in [0..50]]; // _G. C. Greubel_, Aug 29 2018
%Y Cf. A001620, A293352, A293353.
%K nonn,easy
%O 0,3
%A _Clark Kimberling_, Oct 09 2017
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