A153712 Numbers k such that the fractional part of Pi^k is greater than 1-(1/k).

1, 2, 15, 22, 58, 109, 157, 1030, 1071, 1274, 2008, 2322, 5269, 151710

Offset

1,2

Comments

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

The next such number must be greater than 100000.

a(15) > 300000. - Robert Price, Mar 25 2019

Links

Table of n, a(n) for n=1..14.

Example

a(3) = 15, since fract(Pi^15) = 0.969... > 0.933... = 1 - (1/15), but fract(Pi^k) <= 1 - (1/k) for 3 <= k <= 14.

Mathematica

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

Crossrefs

Cf. A153664, A153672, A153680, A153688, A153696, A153704, A153716, A154130, A153720.

Cf. A001672.

Sequence in context: A075722 A169597 A280288 * A153711 A116049 A184236

Adjacent sequences: A153709 A153710 A153711 * A153713 A153714 A153715

Keyword

nonn,more

Author

Hieronymus Fischer, Jan 06 2009

Extensions

a(14) from Robert Price, Mar 25 2019

Status

approved