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

Offset: 1

Author

James R. Buddenhagen, Feb 27 2005

Keywords

• easy
• nonn
• base

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.

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Biquadratic Number.

Crossrefs

Cf. A062941, A049415.

Column k=4 of A216653.

Programs

Maple

r:= proc(n, k) local b; b:= iroot(n, k); b+`if`(b^k 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 *)

Extensions

More terms from Robert G. Wilson v, Mar 03 2005