%I #13 Mar 13 2019 23:41:08

%S 2,16,22,176,222,1776,2222,17776,22222,177776,222222,1777776,2222222,

%T 17777776,22222222,177777776,222222222,1777777776,2222222222,

%U 17777777776,22222222222,177777777776,222222222222,1777777777776,2222222222222,17777777777776

%N Numbers n such that the cardinality of (natural numbers <=n with a first digit of 1) = n/2.

%C This is conceptually related to Benford's law.

%H <a href="/index/Be#Benford">Index entries for sequences related to Benford's law</a>

%F a(n) for odd values of n is simply "2" repeated (n+1)/2 times (sum as i=1->(n/2) of 10^(i-1)). For even values of n, it's a(n-1)*8.

%F G.f.: 2*(1+8*x)/((1-x)*(1+x)*(1-10*x^2)). [_Joerg Arndt_, Aug 14 2013]

%o (PARI) Vec(2*(1+8*x)/((1-x)*(1+x)*(1-10*x^2))+O(x^66)) \\ _Joerg Arndt_, Aug 14 2013

%K base,easy,nonn

%O 1,1

%A _Michael Turniansky_, Aug 14 2013