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Numbers k such that k and k^2 use only the digits 1, 4, 6 and 9.
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%I #17 May 01 2024 11:29:39

%S 1,4,14,119,4119

%N Numbers k such that k and k^2 use only the digits 1, 4, 6 and 9.

%C Generated with DrScheme.

%C From _Pontus von Brömssen_, May 01 2024: (Start)

%C a(6) > 10^43 (if it exists).

%C If k = x*10^m is a term where 1 <= x < 10 and k is not 1 or 119, then 1.1914114169419441614111944144941411111111191 < x < 20/3.

%C (End)

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

%e 4119^2 = 16966161.

%o (PARI) isokd(d) = #setintersect([0,2,3,5,7,8], Set(d)) == 0;

%o isok(k) = isokd(digits(k)) && isokd(digits(k^2)); \\ _Michel Marcus_, Jun 24 2021

%K base,nonn,more

%O 1,2

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