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Numbers which have more different digits than their squares.
2

%I #12 Apr 20 2023 14:55:11

%S 109,173,235,264,1049,1235,1485,1489,1490,1498,1703,1730,1823,1834,

%T 2107,2108,2350,2357,2435,2538,2581,2640,2830,2978,2980,2983,3114,

%U 3148,3157,3408,4827,5162,5470,5480,5962,6380,6498,6742,6912,7450,8130,8167,9235,9607

%N Numbers which have more different digits than their squares.

%C The sequence is infinite since for every element k with '0' as last digit or no '0' at all every k*10^m is also in it.

%H Michael S. Branicky, <a href="/A061277/b061277.txt">Table of n, a(n) for n = 1..10000</a>

%e 3114 is okay, since it has three different digits while 3114^2 = 9696996 has only two.

%t Select[Range[6000],Count[DigitCount[#],0]<Count[DigitCount[#^2],0]&] (* _Harvey P. Dale_, Jul 19 2019 *)

%o (PARI) isok(n) = length(Set(digits(n, 10))) > length(Set(digits(n^2, 10))) \\ _Michel Marcus_, Jul 22 2013

%o (Python)

%o def ok(n): return len(set(str(n))) > len(set(str(n**2)))

%o print([k for k in range(10**4) if ok(k)]) # _Michael S. Branicky_, Apr 20 2023

%K nonn,base

%O 1,1

%A Ulrich Schimke (ulrschimke(AT)aol.com)

%E a(36) and beyond from _Michael S. Branicky_, Apr 20 2023