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A102831

Number of n-digit 4th powers.

2, 2, 2, 4, 8, 14, 25, 43, 78, 139, 246, 437, 779, 1384, 2461, 4376, 7783, 13840, 24612, 43765, 77828, 138400, 246114, 437658, 778280, 1383998, 2461136, 4376586, 7782795, 13839982, 24611356, 43765867, 77827942, 138399825, 246113559

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OFFSET

1,1

COMMENTS

The number 0 is considered a 1-digit 4th power. This is consistent with A062941 which considers 0 a 1-digit cube, but is inconsistent with A049415 which does not consider 0 a 1-digit square.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Biquadratic Number.

EXAMPLE

a(1)=2 because there are 2 1-digit 4th powers, 0 and 1.

MAPLE

r:= proc(n, k) local b; b:= iroot(n, k); b+`if`(b^k<n, 1, 0) end:

a:= n-> r(10^n, 4) -r(10^(n-1), 4) +`if`(n=1, 1, 0):

seq(a(n), n=1..50); # Alois P. Heinz, Sep 12 2012

MATHEMATICA

f[n_] := If[n == 1, 2, Ceiling[ Sqrt[ Sqrt[10^n]]] - Ceiling[ Sqrt[ Sqrt[10^(n - 1)]]]]; Table[ f[n], {n, 34}] (* Robert G. Wilson v, Mar 03 2005 *)

CROSSREFS