A137100 - OEIS

%I #16 May 10 2024 11:28:58

%S 2,26,474,4762

%N Numbers k such that k and k^2 use only the digits 2, 4, 6 and 7.

%C Generated with DrScheme.

%C No additional terms through 7777777777. - _Harvey P. Dale_, Dec 08 2015

%C No additional terms to 10^26. - _Robert Israel_, Nov 24 2023

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

%e 4762^2 = 22676644.

%p Good:= {2,4,6,7}:

%p R:= 2:

%p G[1]:= select(t -> member(t^2 mod 10,Good), Good):

%p for d from 2 to 26 do

%p   G[d]:= select(t -> member(floor((t^2 mod 10^d)/10^(d-1)),Good), map(t -> seq(10^(d-1)*i+t, i=Good), G[d-1]));

%p   for t in G[d] do

%p     if convert(convert(t^2,base,10),set) subset Good then  R:= R,t fi

%p od

%p od:

%p R; # _Robert Israel_, Nov 24 2023

%t With[{c={2,4,6,7}},Select[Flatten[Table[FromDigits/@Tuples[c,n],{n,5}]],SubsetQ[c,IntegerDigits[#^2]]&]] (* _Harvey P. Dale_, Dec 08 2015 *)

%K base,nonn,more

%O 1,1

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