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A333332
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Positive numbers k at which min{abs(2^k - 10^y)/10^y: y in Z} reaches a new minimum.
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0
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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