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A344634 Numbers k such that half the numbers from 0 to k inclusive contain the digit "0". 2
1, 10761677, 14958585, 14960717, 14961735, 15013205, 15588833, 15590573, 15591959, 15591961, 15592031, 15592229, 15592231, 15603695, 15633495, 15633503, 15633517, 16076087, 16263743, 20327615 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 8 15:28 EST 2023. Contains 360149 sequences. (Running on oeis4.)