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 A333332 Positive numbers k at which min{abs(2^k - 10^y)/10^y: y in Z} reaches a new minimum. 0
 1, 2, 3, 10, 93, 196, 485, 2136, 13301, 28738, 42039, 70777, 254370, 325147, 6107016, 6432163, 44699994, 51132157, 146964308, 198096465, 345060773, 1578339557, 1923400330, 82361153417, 496090320832, 578451474249, 2809896217828, 6198243909905, 21404627947543 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS Table of n, a(n) for n=1..29. PROG (Python) def closest_powers_of_2_to_10(n): smallest_error = 1 a = [] r = 0.2 # ratio test starts at 2/10 k = 1 while len(a) < n: error = abs(1-r) if error < smallest_error: smallest_error = error a.append(k) print(a) if r<1.0: r *= 2 else: r /= 10 k -= 1 # need to check the other power of 10 k += 1 return a print(closest_powers_of_2_to_10(20)) CROSSREFS Cf. A046104, A073733. Sequence in context: A088222 A184249 A270356 * A229220 A155148 A076927 Adjacent sequences: A333329 A333330 A333331 * A333333 A333334 A333335 KEYWORD nonn AUTHOR Zachary Hervieux-Moore, Mar 15 2020 EXTENSIONS More terms from Hugo Pfoertner, May 01 2020 STATUS approved

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Last modified September 14 06:05 EDT 2024. Contains 375911 sequences. (Running on oeis4.)