A344634 - OEIS

%I #29 Jun 21 2021 03:17:24

%S 1,10761677,14958585,14960717,14961735,15013205,15588833,15590573,

%T 15591959,15591961,15592031,15592229,15592231,15603695,15633495,

%U 15633503,15633517,16076087,16263743,20327615

%N Numbers k such that half the numbers from 0 to k inclusive contain the digit "0".

%C Andrew Hilton (see Ref.) refers to these as "half-zero" numbers.

%D Andrew Hilton, 101 Puzzles to Solve on your Microcomputer, 1984, HARRAP, page 57.

%e 1 is a term since among the numbers 0,1 exactly half contain a digit "0".

%e 10761677 is a term since among the numbers 0,1,2,...,10761677 exactly half contain a digit "0".

%o (Python 3)

%o z=0

%o z_s = str(z)

%o counts=0

%o for x in trange (0,100000000000):

%o     x_s = str(x)

%o     if z_s in x_s:

%o         counts += 1

%o     if counts / (x+1) == 0.5:

%o         print(z,x)

%o (Python)

%o def afind(limit):

%o   count0 = [0, 1]

%o   for k in range(1, limit+1):

%o     count0['0' in str(k)] += 1

%o     if count0[0] == count0[1]: print(k, end=", ")

%o afind(3*10**7) # _Michael S. Branicky_, May 25 2021

%Y Cf. A016189, A334474, A344636.

%K nonn,base,fini,full

%O 1,2

%A _Glen Gilchrist_, May 25 2021