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 A153677 Minimal exponents m such that the fractional part of (1024/1000)^m obtains a minimum (when starting with m=1). 12
 1, 68, 142, 341, 395, 490, 585, 1164, 1707, 26366, 41358, 46074, 120805, 147332, 184259, 205661, 385710, 522271, 3418770, 3675376, 9424094 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Recursive definition: a(1)=1, a(n) is the least positive integer m such that the fractional part of (1024/1000)^m is less than the fractional part of (1024/1000)^k for all k, 1 <= k < m. a(21) >= 4.5*10^6. - David A. Corneth, Mar 15 2019 a(22) > 10^7. Robert Price, Mar 16 2019 LINKS Table of n, a(n) for n=1..21. FORMULA Recursion: a(1):=1, a(k):=min{ m>1 | fract((1024/1000)^m) < fract((1024/1000)^a(k-1))}, where fract(x) = x-floor(x). EXAMPLE a(2)=68, since fract((1024/1000)^68) = 0.016456..., but fract((1024/1000)^k) >= 0.024 for 1 <= k <= 67; thus fract((1024/1000)^68) < fract((1024/1000)^k) for 1 <= k < 68. MATHEMATICA \$MaxExtraPrecision = 10000; p = .999; Select[Range[1, 50000], If[FractionalPart[(1024/1000)^#] < p, p = FractionalPart[(1024/1000)^#]; True] &] (* Robert Price, Mar 15 2019 *) PROG (PARI) upto(n) = my(res = List(), r = 1, p = 1); for(i=1, n, c = frac(p *= 1.024); if(c

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Last modified December 3 22:01 EST 2023. Contains 367540 sequences. (Running on oeis4.)