A052044 Numbers k such that k^3 lacks the digit zero in its decimal expansion.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 35, 36, 38, 39, 41, 44, 45, 46, 49, 51, 53, 54, 55, 56, 57, 58, 61, 62, 64, 65, 66, 68, 71, 72, 75, 76, 77, 78, 81, 82, 83, 85, 88, 91, 92, 95, 96, 97, 98, 104, 105, 108, 111

Offset: 1

Author

Patrick De Geest, Dec 15 1999

Keywords

• nonn
• base

Comments

This sequence is infinite since A052427 is a subsequence. - Amiram Eldar, Nov 23 2020

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Logarithmic scatterplot of (n, a(n+1)-a(n)) for n = 1..1000000

Crossrefs

Cubes: A052045, A051750, A051751, A051832, A051833, A052427.

Squares: A052040, A052041, A052042, A052043.

Programs

Mathematica

Select[Range[120],DigitCount[#^3,10,0]==0&] (* Harvey P. Dale, Oct 24 2011 *)

PARI

is(n)=vecmin(digits(n^3))>0 \\ Charles R Greathouse IV, Oct 11 2013

Formula

a(n) = A052045(n)^(1/3). - Amiram Eldar, Nov 23 2020