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Numbers whose square contains no loops in its digits (assumes 1, 2, 3, 5, 7 have no loops and 0, 4, 6, 8, 9 do).
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%I #20 Jul 30 2021 08:52:10

%S 1,5,11,15,35,39,61,85,111,115,165,189,235,239,335,365,389,415,461,

%T 485,611,715,1061,1085,1165,1235,1239,1489,1585,1665,1765,1885,2261,

%U 2285,2715,3335,3365,3489,3511,3515,3635,3711,3915,3939,3965,4139,4211,4715

%N Numbers whose square contains no loops in its digits (assumes 1, 2, 3, 5, 7 have no loops and 0, 4, 6, 8, 9 do).

%H Giovanni Resta, <a href="/A034905/b034905.txt">Table of n, a(n) for n = 1..10000</a>

%e 13^2 = 169 contains a 6 and a 9, so 13 does not belong to the sequence.

%t Select[Range[5000],ContainsAll[{1,2,3,5,7},IntegerDigits[#^2]]&] (* _Giorgos Kalogeropoulos_, Jul 30 2021 *)

%Y Cf. A031153, A001742.

%K nonn,base

%O 1,2

%A _J. Lowell_