

A052040


Numbers n such that n^2 lacks the digit zero in its decimal expansion.


18



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


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.
Sequence in context: A067251 A052382 A055572 * A328781 A069570 A279367
Adjacent sequences: A052037 A052038 A052039 * A052041 A052042 A052043


KEYWORD

nonn,base


AUTHOR

Patrick De Geest, Dec 15 1999


STATUS

approved



