cp's OEIS Frontend

A333332 Positive numbers k at which min{abs(2^k - 10^y)/10^y: y in Z} reaches a new minimum.

%I A333332 #40 May 02 2020 07:00:31
%S A333332 1,2,3,10,93,196,485,2136,13301,28738,42039,70777,254370,325147,
%T A333332 6107016,6432163,44699994,51132157,146964308,198096465,345060773,
%U A333332 1578339557,1923400330,82361153417,496090320832,578451474249,2809896217828,6198243909905,21404627947543
%N A333332 Positive numbers k at which min{abs(2^k - 10^y)/10^y: y in Z} reaches a new minimum.
%C A333332 If {k(n)/y(n)} are the convergent fractions to log_2(10), then numerators k(n) are in A073733, and denominators y(n) are in A046104; now, k and y means k(n) and y(n): k/y ~ log_2(10) <==> 2^(k/y) ~ 10 <==> 2^k ~ 10^y <==> lim_{n->oo} (2^k / 10^y) = 1 <==> lim_{n->oo} abs(2^k/10^y - 1) = 0 <==> lim_{n->oo} abs(2^k - 10^y)/10^y = 0, that corresponds to the name. - _Bernard Schott_, Apr 29 2020
%o A333332 (Python)
%o A333332 def closest_powers_of_2_to_10(n):
%o A333332   smallest_error = 1
%o A333332   a = []
%o A333332   r = 0.2 # ratio test starts at 2/10
%o A333332   k = 1
%o A333332   while len(a) < n:
%o A333332     error = abs(1-r)
%o A333332     if error < smallest_error:
%o A333332       smallest_error = error
%o A333332       a.append(k)
%o A333332       print(a)
%o A333332     if r<1.0:
%o A333332       r *= 2
%o A333332     else:
%o A333332       r /= 10
%o A333332       k -= 1 # need to check the other power of 10
%o A333332     k += 1
%o A333332   return a
%o A333332 print(closest_powers_of_2_to_10(20))
%Y A333332 Cf. A046104, A073733.
%K A333332 nonn
%O A333332 1,2
%A A333332 _Zachary Hervieux-Moore_, Mar 15 2020
%E A333332 More terms from _Hugo Pfoertner_, May 01 2020