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

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

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