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A078255 Squares with distinct digits. To make an infinite sequence, we also include m-digit numbers in which each digit occurs no more than ceiling(m/10) times.

%I A078255 #20 Oct 30 2023 01:51:56
%S A078255 0,1,4,9,16,25,36,49,64,81,169,196,256,289,324,361,529,576,625,729,
%T A078255 784,841,961,1024,1089,1296,1369,1764,1849,1936,2304,2401,2601,2704,
%U A078255 2809,2916,3025,3249,3481,3721,4096,4356,4761,5041,5184,5329,5476,6084,6241
%N A078255 Squares with distinct digits. To make an infinite sequence, we also include m-digit numbers in which each digit occurs no more than ceiling(m/10) times.
%C A078255 The largest square with no digit repeated more than m times, for m = 1 to 4: 99066^2 = 9814072356; 9994363488^2 = 99887301530267526144; 999944387118711^2 = 999888777330214565264406301521; 99999444387327303945^2 = 9999888877774166231060453541302412563025.
%C A078255 There are exactly 87 10-digit squares with distinct digits. - _Harvey P. Dale_, Sep 06 2020
%H A078255 Michael S. Branicky, <a href="/A078255/b078255.txt">Table of n, a(n) for n = 1..10000</a>
%e A078255 100116^2 = 10023213456 is a term because it has 11 digits,
%e A078255 ceiling(11/10) = 2 and no digit occurs more than twice. This is the first term after 9814072356.
%t A078255 Select[Range[0,80]^2,Max[DigitCount[#]]==1&] (* The program only selects numbers with no more than 10 digits, and even that would require changing the high Range constant to 100000. *) (* _Harvey P. Dale_, Sep 06 2020 *)
%o A078255 (Python)
%o A078255 from itertools import count, islice
%o A078255 def c(n): return all((s:=str(n)).count(d)<=(len(s)-1)//10+1 for d in "0123456789")
%o A078255 def agen(): yield from filter(c, (k*k for k in count(0)))
%o A078255 print(list(islice(agen(), 50))) # _Michael S. Branicky_, Oct 29 2023
%Y A078255 Cf. A075309.
%K A078255 base,nonn,easy
%O A078255 1,3
%A A078255 _Amarnath Murthy_, Nov 24 2002
%E A078255 Edited and extended by _David Wasserman_, Jun 27 2006