A034060 - OEIS

%I #25 Jun 22 2023 06:04:14

%S 33,2,3,4,6,8,11,15,19,25,41,42,43,44,2,46,48,49,50,51,52,53,54,56,3,

%T 58,59,61,62,63,65,4,68,69,71,72,74,5,77,78,80,82,83,6,87,89,91,7,94,

%U 96,98,8,102,104,106,9,110,113,10,117,119,11

%N a(n) is the least k (not a 5th power) such that the decimal part of k^(1/5) starts with n.

%H Robert Israel, <a href="/A034060/b034060.txt">Table of n, a(n) for n = 0..9999</a>

%e a(0)=33 because 33^(1/5) = 2.0123466... and 0123466... starts with 0, and there is no k < 33 whose 5th root has this property.

%e a(1)=2 because 2^(1/5) = 1.1486983... and 1486983... starts with 1, and there is no k < 2 whose 5th root has this property.

%p d:= 2: # for a(0) .. a(10^d-1)

%p V:= Array(0..10^d-1): V[0]:= 33: count:= 1:

%p for x from 2 while count < 10^d do

%p   v:= floor(10^d*x^(1/5)) mod 10^d;

%p if v < 10^(d-1) then next fi;

%p   for i from 1 to d do

%p     w:= floor(v/10^(d-i));

%p     if V[w] = 0 then V[w]:= x; count:= count+1; fi

%p   od

%p od:

%p convert(V,list); # _Robert Israel_, Jun 20 2023

%Y Cf. A034070, A034080.

%K nonn,base

%O 0,1

%A _Patrick De Geest_, Sep 15 1998

%E Edited by _Robert Israel_, Jun 21 2023