A100323 Numbers k such that the decimal expansion of Pi^k begins (after the decimal point) with k.

1, 4, 75, 9424, 12669, 331783

Offset

1,2

Comments

The terms of this sequence are related to those in A100322, but do not necessarily appear in that sequence since A100322(n) is defined as the smallest positive integer k such that the digits of the fractional part of Pi^k begin with n.

Links

Table of n, a(n) for n=1..6.

Example

Pi^1 = 3.1...;
Pi^4 = 97.4...;
Pi^75 = 19330382693312372796273669213182810875.75...

Mathematica

p = N[Pi, 10^4]; f[n_] := Block[{r = RealDigits[p^n, 10, Max[5, n]]}, e = r[[2]]; FromDigits[ Take[r[[1]], {e + 1, e + 1 + Floor[ Log[10, n]]} ]]]; Do[ If[ f[n] == n, Print[n]], {n, 10^4}] (* Robert G. Wilson v, Nov 16 2004 *)

Crossrefs

Cf. A100322.

Sequence in context: A374884 A120248 A191505 * A262073 A067921 A317903

Adjacent sequences: A100320 A100321 A100322 * A100324 A100325 A100326

Keyword

base,nonn,more

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 16 2004

Extensions

a(6) from Jon E. Schoenfield, Mar 28 2015

Status

approved