A052040 - OEIS

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

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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.