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Numbers k such that k and k^2 use only the digits 0, 1, 4 and 5.
1

%I #11 Jul 05 2021 09:09:34

%S 0,1,10,100,1000,10000,100000,100501,1000000,1005010,10000000,

%T 10005001,10050100,100000000,100050010,100501000,1000000000,

%U 1000050001,1000500100,1005010000,10000000000,10000500010,10005001000,10050100000,100000000000,100000500001,100005000100,100050010000,100501000000,1000000000000

%N Numbers k such that k and k^2 use only the digits 0, 1, 4 and 5.

%C Generated with DrScheme.

%H Jonathan Wellons, <a href="/A136854/b136854.txt">Table of n, a(n) for n = 1..46</a>

%H Jonathan Wellons, <a href="https://web.archive.org/web/20090206165028/http://jonathanwellons.com/shared-digits/">Tables of Shared Digits</a>

%e 100501000000000^2 = 10100451001000000000000000000.

%t With[{c={0,1,4,5}},Select[FromDigits/@Tuples[c,13],SubsetQ[c, IntegerDigits[ #^2]]&]] (* _Harvey P. Dale_, Apr 15 2018 *)

%Y Cf. A000290.

%K base,nonn

%O 1,3

%A Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008