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A037344 Numbers whose base-2 and base-10 expansions have no digits in common.

%I A037344 #20 Aug 14 2025 09:00:51
%S A037344 2,3,4,5,6,7,8,9,22,23,24,25,26,27,28,29,32,33,34,35,36,37,38,39,42,
%T A037344 43,44,45,46,47,48,49,52,53,54,55,56,57,58,59,62,63,64,65,66,67,68,69,
%U A037344 72,73,74,75,76,77,78,79,82,83,84,85,86,87,88,89,92,93,94,95,96,97,98,99,222
%N A037344 Numbers whose base-2 and base-10 expansions have no digits in common.
%H A037344 Vincenzo Librandi, <a href="/A037344/b037344.txt">Table of n, a(n) for n = 1..1000</a>
%p A037344 isA037344 := proc(n)
%p A037344     local dgs10,dgs2 ;
%p A037344     dgs10 := convert(convert(n,base,10),set) ;
%p A037344     dgs2 := convert(convert(n,base,2),set) ;
%p A037344     if dgs10 intersect dgs2 = {} then
%p A037344         true ;
%p A037344     else
%p A037344         false ;
%p A037344     end if;
%p A037344 end proc:
%p A037344 A037344 := proc(n)
%p A037344     option remember ;
%p A037344     local a;
%p A037344     if n = 1 then
%p A037344         2;
%p A037344     else
%p A037344         for a from procname(n-1)+1 do
%p A037344             if isA037344(a) then
%p A037344                 return a;
%p A037344             end if;
%p A037344         end do;
%p A037344     end if;
%p A037344 end proc:
%p A037344 seq(A037344(n),n=1..200) ; # _R. J. Mathar_, Aug 14 2025
%t A037344 Select[Range[100],Intersection[IntegerDigits[#,2],IntegerDigits[#,10]]=={}&] (* _Vincenzo Librandi_, Jun 06 2012 *)
%Y A037344 Not the same as A062998 or A387032.
%K A037344 nonn,base
%O A037344 1,1
%A A037344 _Clark Kimberling_