%I #32 Nov 23 2020 02:06:59

%S 1,8,27,64,125,216,343,512,729,1331,1728,2197,2744,3375,4913,5832,

%T 6859,9261,12167,13824,15625,17576,19683,21952,24389,29791,32768,

%U 35937,42875,46656,54872,59319,68921,85184,91125,97336,117649,132651,148877

%N Cubes lacking the digit zero in their decimal expansion.

%C This sequence is infinite since A052427(n)^3 is a term for all n>=0. - _Amiram Eldar_, Nov 23 2020

%H Amiram Eldar, <a href="/A052045/b052045.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Alois P. Heinz)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Zerofree.html">Zerofree</a> [From _Reinhard Zumkeller_, Dec 01 2009]

%F Intersection of A052382 and A000578; A168046(a(n))*A010057(a(n)) = 1. - _Reinhard Zumkeller_, Dec 01 2009

%F a(n) = A052044(n)^3. - _Amiram Eldar_, Nov 23 2020

%p select(t -> not has(convert(t,base,10),0), [seq(m^3,m=1..10^3)]); # _Robert Israel_, Aug 24 2014

%t Select[Range[53]^3, DigitCount[#, 10, 0] == 0 &] (* _Amiram Eldar_, Nov 23 2020 *)

%o (Python)

%o A052045 = [n**3 for n in range(1,10**5) if not str(n**3).count('0')]

%o # _Chai Wah Wu_, Aug 24 2014

%o (PARI) lista(nn) = {for (n=1, nn, if (vecmin(digits(cub=n^3)), print1(cub, ", ")););} \\ _Michel Marcus_, Aug 25 2014

%Y Cubes: A052044, A051750, A051751, A051832, A051833, A052427.

%Y Squares: A052040, A052041, A052042, A052043.

%K nonn,base

%O 1,2

%A _Patrick De Geest_, Dec 15 1999