login
A052040
Numbers whose square is zeroless.
20
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
Cf. A052382.
Sequence in context: A367733 A043095 A055572 * A328781 A069570 A279367
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Dec 15 1999
STATUS
approved