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

Author

Glen Gilchrist, May 25 2021

Keywords

• nonn
• base
• fini
• full

Comments

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

Examples

			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".
		

References

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

Crossrefs

Cf. A016189, A334474, A344636.

Programs

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