A153710 - OEIS

A153710

Numbers k such that the fractional part of Pi^k is less than 1/k.

1, 3, 5, 9, 10, 11, 59, 81, 264, 281, 472, 3592, 10479, 12128, 65875, 118885

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OFFSET

1,2

COMMENTS

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

The next such number must be greater than 100000.

a(17) > 300000. - Robert Price, Mar 25 2019

LINKS

EXAMPLE

a(4) = 9 since fract(Pi^9) = 0.0993... < 1/9, but fract(Pi^k) = 0.3891..., 0.2932..., 0.5310... for 6 <= k <= 8, which all are greater than 1/k.

MATHEMATICA

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

PROG

(PARI) isok(k) = frac(Pi^k) < 1/k; \\ Michel Marcus, Feb 11 2014

CROSSREFS

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

a(16) from Robert Price, Mar 25 2019

STATUS

approved