A344634 Numbers k such that half the numbers from 0 to k inclusive contain the digit "0".

1, 10761677, 14958585, 14960717, 14961735, 15013205, 15588833, 15590573, 15591959, 15591961, 15592031, 15592229, 15592231, 15603695, 15633495, 15633503, 15633517, 16076087, 16263743, 20327615

Offset

1,2

Comments

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

References

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

Links

Table of n, a(n) for n=1..20.

Example

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

Prog

(Python 3)
z=0
z_s = str(z)
counts=0
for x in trange (0, 100000000000):
    x_s = str(x)
    if z_s in x_s:
        counts += 1
    if counts / (x+1) == 0.5:
        print(z, x)
(Python)
def afind(limit):
  count0 = [0, 1]
  for k in range(1, limit+1):
    count0['0' in str(k)] += 1
    if count0[0] == count0[1]: print(k, end=", ")
afind(3*10**7) # Michael S. Branicky, May 25 2021

Crossrefs

Cf. A016189, A334474, A344636.

Sequence in context: A157762 A234390 A237149 * A071370 A203942 A251488

Adjacent sequences: A344631 A344632 A344633 * A344635 A344636 A344637

Keyword

nonn,base,fini,full

Author

Glen Gilchrist, May 25 2021

Status

approved