A293354 The integer k that minimizes |k/2^n - r|, where r = Euler's constant (0.577216...).

1, 1, 2, 5, 9, 18, 37, 74, 148, 296, 591, 1182, 2364, 4729, 9457, 18914, 37828, 75657, 151314, 302627, 605254, 1210509, 2421018, 4842036, 9684072, 19368144, 38736288, 77472575, 154945150, 309890300, 619780601, 1239561202, 2479122403, 4958244807, 9916489614

Offset

0,3

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Formula

a(n) = floor(1/2 + r*2^n), where r = Euler's constant (0.577216...).

a(n) = A293352(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293353(n).

Mathematica

z = 120; r = EulerGamma;
Table[Floor[r*2^n], {n, 0, z}];   (* A293352 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293353 *)
Table[Round[r*2^n], {n, 0, z}];   (* A293354 *)

Prog

(PARI) for(n=0, 50, print1(round(Euler*2^n), ", ")) \\ G. C. Greubel, Aug 29 2018
(Magma) R:= RealField(100); [Round(EulerGamma(R)*2^n) : n in [0..50]]; // G. C. Greubel, Aug 29 2018

Crossrefs

Cf. A001620, A293352, A293353.

Sequence in context: A364525 A077947 A077972 * A293329 A152546 A286713

Adjacent sequences: A293351 A293352 A293353 * A293355 A293356 A293357

Keyword

nonn,easy

Author

Clark Kimberling, Oct 09 2017

Status

approved