|
%I #32 Sep 08 2022 08:44:59
%S 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,
%T 29,31,34,35,36,37,38,39,41,42,43,44,46,54,56,57,58,59,61,62,63,65,66,
%U 67,68,69,72,73,74,75,76,77,79,81,82,83,85,86,87,88,89,91,92,93,94,96
%N Numbers whose square is zeroless.
%C 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
%H Charles R Greathouse IV, <a href="/A052040/b052040.txt">Table of n, a(n) for n = 1..10000</a>
%H Michael Beeler, R. William Gosper, and Rich Schroeppel, <a href="http://www.inwap.com/pdp10/hbaker/hakmem/number.html#item36">"HAKMEM" Item 36</a>, Memo 239, Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, Mass., 1972.
%e From _Jon E. Schoenfield_, Aug 16 2021: (Start)
%e 31 is a term: 31^2 = 961 has no 0's among its digits.
%e 32 is not a term, because 32^2 = 1024. (End)
%t Select[Range[0, 100], DigitCount[#^2, 10, 0]==0 &] (* _Vincenzo Librandi_, Feb 22 2015 *)
%o (PARI) is(n)=vecmin(digits(n^2))>0 \\ _Charles R Greathouse IV_, Oct 11 2013
%o (Magma) [n: n in [1..100] | not 0 in Intseq(n^2)]; // _Vincenzo Librandi_, Feb 22 2015
%Y Squares: A052041, A052042, A052043. Cubes: A051750, A051751, A051832, A051833.
%Y Cf. A052382.
%K nonn,base
%O 1,2
%A _Patrick De Geest_, Dec 15 1999
|
