A344636 Numbers k such that half the numbers from 0 to k inclusive contain the digit "1".

1, 17, 23, 161, 269, 271, 1457, 3397, 3419, 3421, 13121, 44685, 118097, 674909, 674933, 1062881

Offset

1,2

Comments

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

References

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

Links

Table of n, a(n) for n=1..16.

Example

1 is a term since among the numbers 0,1 exactly half contain a digit "1".
17 is a term since among the numbers 0,1,2,...,17 exactly half contain a digit "1".

Mathematica

Select[2Range@2000, Length@Select[Range[0, #-1], MemberQ[IntegerDigits@#, 1]&]==#/2&]-1 (* Giorgos Kalogeropoulos, Jul 28 2021 *)

Prog

(Python 3)
z=1
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(x)

Crossrefs

Cf. A344474, A344634, A343839, A011531, A016189.

Sequence in context: A060252 A127924 A250640 * A108260 A062628 A127907

Adjacent sequences: A344633 A344634 A344635 * A344637 A344638 A344639

Keyword

nonn,base,fini,full

Author

Glen Gilchrist, May 25 2021

Status

approved