A153683 -id:A153683 - cp's OEIS frontend

A153687 Minimal exponents m such that the fractional part of (11/10)^m obtains a maximum (when starting with m=1).

1, 2, 3, 4, 5, 6, 7, 23, 56, 77, 103, 320, 1477, 1821, 2992, 15290, 180168, 410498, 548816, 672732, 2601223

Offset: 1

Hieronymus Fischer, Jan 06 2009

Recursive definition: a(1)=1, a(n) = least number m>a(n-1) such that the fractional part of (11/10)^m is greater than the fractional part of (11/10)^k for all k, 1<=k

The next such number must be greater than 2*10^5.

a(22) > 10^7. Robert Price, Mar 19 2019

			a(8)=23, since fract((11/10)^23)= 0.9543..., but fract((11/10)^k)<0.95 for 1<=k<=22;
thus fract((11/10)^23)>fract((11/10)^k) for 1<=k<23 and 23 is the minimal exponent > 7 with this property.

Cf. A153663, A153671, A153683, A153679, A154130, A153695, A091560, A153711, A153719.

p = 0; Select[Range[1, 50000],
If[FractionalPart[(11/10)^#] > p, p = FractionalPart[(11/10)^#];
True] &] (* Robert Price, Mar 19 2019 *)

A153687_list, m, n, k, q = [], 1, 11, 10, 0
while m < 10**4:
    r = n % k
    if r > q:
        q = r
        A153687_list.append(m)
    m += 1
    n *= 11
    k *= 10
    q *= 10 # Chai Wah Wu, May 16 2020

Recursion: a(1):=1, a(k):=min{ m>1 | fract((11/10)^m) > fract((11/10)^a(k-1))}, where fract(x) = x-floor(x).

a(18)-a(21) from Robert Price, Mar 19 2019

A153675 Greatest number m such that the fractional part of (101/100)^A153671(m) >= 1-(1/m).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 7, 9, 11, 13, 19, 30, 76, 81, 238, 913, 1334, 4645, 6812, 17396, 351085, 552184

Offset: 1

Hieronymus Fischer, Jan 06 2009

nonn

			a(5)=1, since 1-(1/2)=0.5>fract((101/100)^A153671(5))=fract((101/100)^5)=0.0510...>=1-(1/1).

Cf. A153663, A154130, A153667, A153683, A153691, A153699, A153707, A153715, A153723.

a(n):=floor(1/(1-fract((101/100)^A153671(n)))), where fract(x) = x-floor(x).

A153691 Greatest number m such that the fractional part of (11/10)^A153687(m) >= 1-(1/m).

Original entry on oeis.org

1, 1, 1, 1, 2, 4, 19, 21, 28, 151, 200, 709, 767, 5727, 15908, 162819, 302991

Offset: 1

Hieronymus Fischer, Jan 06 2009

			a(6)=4, since 1-(1/5)=0.8>fract((11/10)^A153687(6))=fract((11/10)^6)=0.771...>=1-(1/4).

Cf. A153663, A153671, A153679, A153683, A154130, A153699, A153707, A153715, A153723.

a(n):=floor(1/(1-fract((11/10)^A153687(n)))), where fract(x) = x-floor(x).

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A153687 Minimal exponents m such that the fractional part of (11/10)^m obtains a maximum (when starting with m=1).

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A153675 Greatest number m such that the fractional part of (101/100)^A153671(m) >= 1-(1/m).

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A153691 Greatest number m such that the fractional part of (11/10)^A153687(m) >= 1-(1/m).

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