A052045 Cubes lacking the digit zero in their decimal expansion.

1, 8, 27, 64, 125, 216, 343, 512, 729, 1331, 1728, 2197, 2744, 3375, 4913, 5832, 6859, 9261, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 29791, 32768, 35937, 42875, 46656, 54872, 59319, 68921, 85184, 91125, 97336, 117649, 132651, 148877

Offset: 1

Author

Patrick De Geest, Dec 15 1999

Keywords

• nonn
• base

Comments

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Alois P. Heinz)
• Eric Weisstein's World of Mathematics, Zerofree [From _Reinhard Zumkeller_, Dec 01 2009]

Crossrefs

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

Squares: A052040, A052041, A052042, A052043.

Programs

Maple

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

Mathematica

Select[Range[53]^3, DigitCount[#, 10, 0] == 0 &] (* Amiram Eldar, Nov 23 2020 *)

PARI

lista(nn) = {for (n=1, nn, if (vecmin(digits(cub=n^3)), print1(cub, ", ")););} \\ Michel Marcus, Aug 25 2014

Python

A052045 = [n**3 for n in range(1,10**5) if not str(n**3).count('0')]
# Chai Wah Wu, Aug 24 2014

Formula

Intersection of A052382 and A000578; A168046(a(n))*A010057(a(n)) = 1. - Reinhard Zumkeller, Dec 01 2009

a(n) = A052044(n)^3. - Amiram Eldar, Nov 23 2020