A153720 Numbers k such that the fractional part of (Pi-2)^k is greater than 1-(1/k).

1, 5, 8, 85, 911, 2921, 4491, 11543, 15724, 27683, 29921, 37276, 126659

Offset: 1

Author

Hieronymus Fischer, Jan 06 2009

Keywords

• nonn
• more

Comments

Numbers k such that fract((Pi-2)^k) > 1-(1/k), where fract(x) = x-floor(x).

The next such number must be greater than 200000.

a(14) > 300000. - Robert Price, Mar 26 2019

Examples

			a(3) = 8, since fract((Pi-2)^8) = 0.8846247315... > 0.875 = 1 - (1/8), but fract((Pi-2)^k) = 0.2134..., 0.5268... <= 1 - (1/k) for 6 <= k <= 7.
		

Crossrefs

Cf. A153664, A153672, A153680, A153688, A153696, A153704, A153712, A153724, A154130.

Programs

Mathematica

Select[Range[1000], N[FractionalPart[(Pi - 2)^#], 100] > 1 - (1/#) &] (* G. C. Greubel, Aug 25 2016 *)