A153689 -id:A153689 - cp's OEIS frontend

A153685 Minimal exponents m such that the fractional part of (11/10)^m obtains a minimum (when starting with m=1).

1, 17, 37, 237, 599, 615, 6638, 13885, 1063942, 9479731

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 less 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(11) > 10^7. Robert Price, Mar 19 2019

			a(2)=17, since fract((11/10)^17)=0.05447.., but fract((11/10)^k)>=0.1 for 1<=k<=16; thus fract((11/10)^17)<fract((11/10)^k) for 1<=k<17.

Cf. A081464, A153669, A153689, A153677, A154130, A153693, A153701, A137994, A153717.

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

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(9)-a(10) from Robert Price, Mar 19 2019

A153673 Greatest number m such that the fractional part of (101/100)^A153669(n) <= 1/m.

Original entry on oeis.org

100, 147, 703, 932, 1172, 3389, 7089, 8767, 11155, 17457, 20810, 25355, 1129226, 1741049, 1960780, 2179637, 2859688, 11014240, 75249086, 132665447, 499298451

Offset: 1

Hieronymus Fischer, Jan 06 2009

			a(2)=147 since 1/148<fract((101/100)^A153669(2))=fract((101/100)^70)=0.00676...<=1/147.

Cf. A154130, A153669, A153665, A153681, A153689, A153697, A153705, A153713, A153721.

A153669 = {1, 70, 209, 378, 1653, 2697, 4806, 13744, 66919, 67873,
   75666, 81125, 173389, 529938, 1572706, 4751419, 7159431, 7840546,
   15896994, 71074288, 119325567};
Table[fp = FractionalPart[(101/100)^A153669[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A153669]}] (* Robert Price, Mar 25 2019 *)

a(n) = floor(1/fract((101/100)^A153669(n))), where fract(x) = x-floor(x).

a(15)-a(21) from Robert Price, Mar 25 2019

A153681 Greatest number m such that the fractional part of (1024/1000)^A153677(n) <= 1/m.

Original entry on oeis.org

41, 60, 76, 116, 233, 463, 718, 1350, 12472, 13733, 17428, 27955, 32276, 41155, 62437, 69643, 111085, 811799, 2656810, 11462221, 56414953

Offset: 1

Hieronymus Fischer, Jan 06 2009

			a(2)=60 since 1/61 < fract((1024/1000)^A153677(2)) = fract((1024/1000)^68) = 0.0164... <= 1/60.

Cf. A081464, A153669, A153677, A154130, A153689, A153697, A153705, A153713, A153721.

A153677 = {1, 68, 142, 341, 395, 490, 585, 1164, 1707, 26366, 41358,
   46074, 120805, 147332, 184259, 205661, 385710, 522271, 3418770,
   3675376, 9424094};
Table[fp = FractionalPart[(1024/1000)^A153677[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A153677]}] (* Robert Price, Mar 25 2019 *)

a(n) = floor(1/fract((1024/1000)^A153677(n))), where fract(x) = x-floor(x).

a(18)-a(21) from Robert Price, Mar 25 2019

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A153685 Minimal exponents m such that the fractional part of (11/10)^m obtains a minimum (when starting with m=1).

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A153673 Greatest number m such that the fractional part of (101/100)^A153669(n) <= 1/m.

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Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula

Extensions

A153681 Greatest number m such that the fractional part of (1024/1000)^A153677(n) <= 1/m.

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Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula

Extensions