%I #9 Jun 13 2020 15:06:19

%S 6,76,776,7776,67776,667776,6667776,66667776,766667776,6766667776,

%T 66766667776,666766667776,7666766667776,77666766667776,

%U 777666766667776,7777666766667776,77777666766667776,777777666766667776

%N a(n) contains n digits (either '6' or '7') and is divisible by 2^n.

%H Ray Chandler, <a href="/A053337/b053337.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n)=a(n-1)+10^(n-1)*(6+[a(n-1)/2^(n-1) mod 2]) i.e. a(n) ends with a(n-1); if (n-1)-th term is divisible by 2^n then n-th term begins with a 6, if not then n-th term begins with a 7.

%t Table[Select[FromDigits/@Tuples[{6,7},n],Divisible[#,2^IntegerLength[ #]]&], {n,18}]//Flatten (* _Harvey P. Dale_, Jul 10 2016 *)

%Y Cf. A023409, A050621, A050622, A035014.

%K base,nonn

%O 1,1

%A _Henry Bottomley_, Mar 06 2000