A053316 - OEIS

%I #8 Oct 27 2019 17:30:16

%S 2,32,232,3232,23232,223232,2223232,32223232,232223232,3232223232,

%T 23232223232,323232223232,3323232223232,23323232223232,

%U 323323232223232,3323323232223232,33323323232223232,333323323232223232

%N a(n) contains n digits (either '2' or '3') and is divisible by 2^n.

%H Robert Israel, <a href="/A053316/b053316.txt">Table of n, a(n) for n = 1..999</a>

%F a(n) = a(n-1) + 10^(n-1)*(2 + (a(n-1)/2^(n-1) mod 2)), i.e., a(n) ends with a(n-1); if a(n-1) is divisible by 2^n then a(n) begins with a 2, if not then a(n) begins with a 3.

%p A[1]:= 2:

%p for n from 2 to 100 do

%p    if A[n-1] mod 2^n = 0 then A[n]:= A[n-1]+2*10^(n-1)

%p    else A[n]:= A[n-1]+3*10^(n-1)

%p      fi

%p od:

%p seq(A[i],i=1..100); # _Robert Israel_, Oct 27 2019

%Y Cf. A023397, A050621, A050622, A035014.

%K base,nonn

%O 1,1

%A _Henry Bottomley_, Mar 06 2000

%E Formula corrected by _Robert Israel_, Oct 27 2019