A052040 Numbers whose square is zeroless.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 46, 54, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 96

Offset

1,2

Comments

This sequence is infinite, since 33...334^2 = 11...11155...556, for example. This answers an open problem stated in HAKMEM. - Karl W. Heuer, Aug 19 2015

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Michael Beeler, R. William Gosper, and Rich Schroeppel, "HAKMEM" Item 36, Memo 239, Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, Mass., 1972.

Example

From Jon E. Schoenfield, Aug 16 2021: (Start)
31 is a term: 31^2 = 961 has no 0's among its digits.
32 is not a term, because 32^2 = 1024. (End)

Mathematica

Select[Range[0, 100], DigitCount[#^2, 10, 0]==0 &] (* Vincenzo Librandi, Feb 22 2015 *)

Prog

(PARI) is(n)=vecmin(digits(n^2))>0 \\ Charles R Greathouse IV, Oct 11 2013
(Magma) [n: n in [1..100] | not 0 in Intseq(n^2)]; // Vincenzo Librandi, Feb 22 2015

Crossrefs

Squares: A052041, A052042, A052043. Cubes: A051750, A051751, A051832, A051833.

Cf. A052382.

Sequence in context: A367733 A043095 A055572 * A328781 A069570 A279367

Adjacent sequences: A052037 A052038 A052039 * A052041 A052042 A052043

Keyword

nonn,base

Author

Patrick De Geest, Dec 15 1999

Status

approved