%I #28 May 10 2020 23:02:48

%S 0,1,3,2,6,22,36,28,156,412,24,1048,3096,1808,6384,22768,34464,31072,

%T 162144,424288,48576,1097152,3194304,1611392,6777216,23554432,

%U 32891136,34217728,168435456,436870912,73741824,1147483648,3294967296,1410065408,7179869184,24359738368

%N Distance of closest integer power of 10 to the n-th power of 2.

%C a(n) is a measure for how well powers of 2 may be approximated by powers of 10. It is e.g. relevant to unit conventions for the magnitude of data (e.g. 1 megabyte is approximately 1 mebibyte). The closely related sequence of distances of the closest integer power of 2 to the n-th power of 10 gives a measure for the precision of floating point expressions in computing applications.

%H Alois P. Heinz, <a href="/A334588/b334588.txt">Table of n, a(n) for n = 0..3322</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Floating-point_arithmetic">Floating-point arithmetic</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Mebibyte">Mebibyte</a>

%e For n=2, a(2) = |4-1| = 3.

%e For n=10, a(10) = min(|2^10-10^3|,|2^10-10^4|) = |1024-1000| = 24.

%p a:= n-> (m-> (p-> min(m-10^p, 10^(p+1)-m))(ilog10(m)))(2^n):

%p seq(a(n), n=0..37); # _Alois P. Heinz_, May 07 2020

%t A[n_] := Min[Abs[(2^n) - 10^Length[IntegerDigits[2^n]]],

%t Abs[(2^n) - 10^(Length[IntegerDigits[2^n]] - 1)]]

%o (PARI) a(n) = my(i=logint(2^n, 10)); min(abs(10^i-2^n), abs(10*10^i-2^n)); \\ _Jinyuan Wang_, May 06 2020

%Y Cf. A000079 (2^n), A011557 (10^n).

%K nonn

%O 0,3

%A _Timon S. Gutleb_, May 06 2020

%E More terms from _Jinyuan Wang_, May 06 2020