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

Author

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

Keywords

• base
• nonn
• more

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.

Examples

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

Crossrefs

Cf. A100322.

Programs

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 *)

Extensions

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