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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
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
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
Column k=4 of A216653.
Sequence in context: A295680 A099768 A285636 * A262568 A183388 A274076
KEYWORD
easy,nonn,base
AUTHOR
EXTENSIONS
More terms from Robert G. Wilson v, Mar 03 2005
STATUS
approved