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A216656 Number of n-digit 6th powers.

%I A216656 #14 Jul 22 2018 19:35:56
%S A216656 2,1,1,1,2,3,5,7,10,15,22,31,47,69,101,148,217,318,468,687,1008,1479,
%T A216656 2171,3187,4678,6867,10078,14793,21714,31870,46780,68664,100784,
%U A216656 147931,217134,318707,467800,686635,1007843,1479311,2171332,3187079,4677993,6866354
%N A216656 Number of n-digit 6th powers.
%C A216656 a(6*k+1) + a(6*k+2) + a(6*k+3) + a(6*k+4) + a(6*k+5) + a(6*k+6) = 9*10^k for k >= 1. - _Robert Israel_, Jul 22 2018
%H A216656 Alois P. Heinz, <a href="/A216656/b216656.txt">Table of n, a(n) for n = 1..1000</a>
%e A216656 a(1) = 2: 0, 1.
%e A216656 a(2) = 1: 64.
%e A216656 a(3) = 1: 729.
%e A216656 a(4) = 1: 4096.
%e A216656 a(5) = 2: 15625, 46656.
%e A216656 a(6) = 3: 117649, 262144, 531441.
%e A216656 a(7) = 5: 1000000, 1771561, 2985984, 4826809, 7529536.
%e A216656 a(8) = 7: 11390625, 16777216, 24137569, 34012224, 47045881, 64000000, 85766121.
%p A216656 r:= proc(n, k) local b; b:= iroot(n, k); b+`if`(b^k<n, 1, 0) end:
%p A216656 a:= n-> r(10^n, 6) -r(10^(n-1), 6) +`if`(n=1, 1, 0):
%p A216656 seq(a(n), n=1..50);
%Y A216656 Column k=6 of A216653.
%K A216656 nonn,base
%O A216656 1,1
%A A216656 _Alois P. Heinz_, Sep 12 2012