A216655 - OEIS

%I #8 Mar 19 2015 20:58:50

%S 2,1,1,3,3,6,10,14,24,36,59,93,147,232,369,585,927,1470,2328,3690,

%T 5849,9270,14692,23285,36904,58490,92699,146919,232850,369042,584894,

%U 926993,1469185,2328502,3690426,5848932,9269933,14691853,23285017,36904265,58489320

%N Number of n-digit 5th powers.

%H Alois P. Heinz, <a href="/A216655/b216655.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1) = 2: 0, 1.

%e a(2) = 1: 32.

%e a(3) = 1: 243.

%e a(4) = 3: 1024, 3125, 7776.

%e a(5) = 3: 16807, 32768, 59049.

%e a(6) = 6: 100000, 161051, 248832, 371293, 537824, 759375.

%e a(7) = 10: 1048576, 1419857, 1889568, 2476099, 3200000, 4084101, 5153632, 6436343, 7962624, 9765625.

%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, 5) -r(10^(n-1), 5) +`if`(n=1, 1, 0):

%p seq(a(n), n=1..50);

%Y Column k=5 of A216653.

%K nonn,base

%O 1,1

%A _Alois P. Heinz_, Sep 12 2012