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A102831 Number of n-digit 4th powers. 17
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 (list; graph; refs; listen; history; text; internal format)
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

Weisstein, Eric W.: Biquadratic Number, (MathWorld).

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

Cf. A062941, A049415.

Column k=4 of A216653.

Sequence in context: A295680 A099768 A285636 * A262568 A183388 A274076

Adjacent sequences:  A102828 A102829 A102830 * A102832 A102833 A102834

KEYWORD

easy,nonn,base

AUTHOR

James R. Buddenhagen, Feb 27 2005

EXTENSIONS

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

STATUS

approved

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)