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%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
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