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Numbers k such that k and k^2 use only the digits 2, 4, 6 and 9.
2

%I #9 Apr 12 2024 09:51:27

%S 2,264,964,494262,494462,4946662,4996962,49944662,499466662,

%T 49994666662,49999296962,499999296962,4999946666662,499999466666662,

%U 49999994666666662,4999999946666666662,499999999466666666662,49999999994666666666662,4999999999946666666666662,499999999999466666666666662

%N Numbers k such that k and k^2 use only the digits 2, 4, 6 and 9.

%C Generated with DrScheme.

%C Includes 5*10^(2*k) - (16*10^k + 14)/3 for k >= 3. The only terms < 10^28 not of that form are 2, 264, 964, 494262, 494462, 4996962, 49944662, 49999296962, and 499999296962. - _Robert Israel_, Nov 24 2023

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

%e 499999296962^2 = 249999296962494262429444.

%p Good := {2, 4, 6, 9}: R:= 2:

%p G[1]:= {2, 4, 6}:

%p for d from 2 to 28 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 od:

%p sort([R]); # _Robert Israel_, Nov 24 2023

%K base,nonn

%O 1,1

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

%E More terms from _Robert Israel_, Nov 24 2023