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%I #17 Feb 11 2024 22:55:22
%S 2,2,2,4,8,14,25,43,78,139,246,437,779,1384,2461,4376,7783,13840,
%T 24612,43765,77828,138400,246114,437658,778280,1383998,2461136,
%U 4376586,7782795,13839982,24611356,43765867,77827942,138399825,246113559
%N Number of n-digit 4th powers.
%C 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.
%H Alois P. Heinz, <a href="/A102831/b102831.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BiquadraticNumber.html">Biquadratic Number</a>.
%e a(1)=2 because there are 2 1-digit 4th powers, 0 and 1.
%p r:= proc(n, k) local b; b:= iroot(n, k); b+`if`(b^k<n, 1, 0) end:
%p a:= n-> r(10^n, 4) -r(10^(n-1), 4) +`if`(n=1, 1, 0):
%p seq(a(n), n=1..50); # _Alois P. Heinz_, Sep 12 2012
%t 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 *)
%Y Cf. A062941, A049415.
%Y Column k=4 of A216653.
%K easy,nonn,base
%O 1,1
%A _James R. Buddenhagen_, Feb 27 2005
%E More terms from _Robert G. Wilson v_, Mar 03 2005
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