A228158 Numbers n such that the cardinality of (natural numbers <=n with a first digit of 1) = n/2.

2, 16, 22, 176, 222, 1776, 2222, 17776, 22222, 177776, 222222, 1777776, 2222222, 17777776, 22222222, 177777776, 222222222, 1777777776, 2222222222, 17777777776, 22222222222, 177777777776, 222222222222, 1777777777776, 2222222222222, 17777777777776

Offset: 1

Author

Michael Turniansky, Aug 14 2013

Keywords

• base
• easy
• nonn

Comments

This is conceptually related to Benford's law.

Links

• Index entries for sequences related to Benford's law

Programs

PARI

Vec(2*(1+8*x)/((1-x)*(1+x)*(1-10*x^2))+O(x^66)) \\ Joerg Arndt, Aug 14 2013

Formula

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.

G.f.: 2*(1+8*x)/((1-x)*(1+x)*(1-10*x^2)). [Joerg Arndt, Aug 14 2013]