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 A153686 Numbers k such that the fractional part of (11/10)^k is less than 1/k. 11
 1, 2, 3, 17, 37, 48, 237, 420, 599, 615, 6638, 13885, 13886, 62963, 1063942, 9479731 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers k such that fract((11/10)^k) < 1/k, where fract(x) = x-floor(x). The next such number must be greater than 2*10^5. a(17) > 10^7. - Robert Price, Mar 19 2019 LINKS EXAMPLE a(4) = 17 since fract((11/10)^17) = 0.05447... < 1/17, but fract((11/10)^k) >= 1/k for 4 <= k <= 16. MATHEMATICA Select[Range[1000], FractionalPart[(11/10)^#] < (1/#) &] (* G. C. Greubel, Aug 24 2016 *) PROG (Python) A153686_list, k, k10, k11 =  [], 1, 10, 11 while k < 10**6:     if (k11 % k10)*k < k10:         A153686_list.append(k)     k += 1     k10 *= 10     k11 *= 11 # Chai Wah Wu, Apr 01 2021 CROSSREFS Cf. A153662, A153670, A153682, A153678, A154130, A153694, A153702, A153710, A153718. Sequence in context: A217688 A263570 A029733 * A042137 A067976 A154316 Adjacent sequences:  A153683 A153684 A153685 * A153687 A153688 A153689 KEYWORD nonn,more AUTHOR Hieronymus Fischer, Jan 06 2009 EXTENSIONS a(15)-a(16) from Robert Price, Mar 19 2019 STATUS approved

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Last modified July 28 09:54 EDT 2021. Contains 346326 sequences. (Running on oeis4.)