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Every digit that appears in k also appears at least once in k^2.
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%I #21 Apr 04 2023 19:16:07

%S 0,1,5,6,10,11,25,27,50,55,60,63,64,66,74,76,95,96,99,100,101,105,110,

%T 111,112,115,116,125,139,142,199,205,211,222,225,232,250,255,261,270,

%U 275,277,278,285,288,305,323,363,364,366,371,376,405,421

%N Every digit that appears in k also appears at least once in k^2.

%H Zak Seidov, <a href="/A029772/b029772.txt">Table of n, a(n) for n = 1..1000</a>

%e 55 is in the list because 55^2 = 3025 and 5 appears in 3025.

%e 323 is in the list because 323^2 = 104329 and 2, 3 appear in 104329.

%t d[n_]:=IntegerDigits[n]; Select[Range[0,421],Complement[d[#],d[#^2]]=={}&] (* _Jayanta Basu_, Jun 02 2013 *)

%o (Magma) [n: n in [0..500] | Intseq(n) subset Intseq(n^2)]; // _Bruno Berselli_, Aug 01 2013

%o (Python)

%o from itertools import count, islice

%o def A029772_gen(startvalue=0): # generator of terms >= startvalue

%o return filter(lambda n:set(str(n)) <= set(str(n**2)), count(max(startvalue,0)))

%o A029772_list = list(islice(A029772_gen(),20)) # _Chai Wah Wu_, Apr 03 2023

%Y See A046827, where it is required that the digits of n appear in n^2 at least as often as they appear in n.

%K nonn,base

%O 1,3

%A _Patrick De Geest_