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

1,2

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]

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

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 *)

Prog

(Python)
A052045 = [n**3 for n in range(1, 10**5) if not str(n**3).count('0')]
# Chai Wah Wu, Aug 24 2014
(PARI) lista(nn) = {for (n=1, nn, if (vecmin(digits(cub=n^3)), print1(cub, ", ")); ); } \\ Michel Marcus, Aug 25 2014

Crossrefs

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

Squares: A052040, A052041, A052042, A052043.

Sequence in context: A000578 A062292 A030295 * A014187 A050750 A100571

Adjacent sequences: A052042 A052043 A052044 * A052046 A052047 A052048

Keyword

nonn,base

Author

Patrick De Geest, Dec 15 1999

Status

approved