A344474 -id:A344474 - cp's OEIS frontend

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

Glen Gilchrist, May 25 2021

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

			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".

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

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

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

A346685 a(n) is the smallest positive integer k such that for all x >= k, at least 50% of the integers in the range 1..x contain n in their decimal expansion. In other words, it is the largest integer k such that exactly half of the integers 1..k have n in their decimal expansion.

Original entry on oeis.org

20327616, 1062880, 2125762, 3188644, 4251526, 5314408, 6377290, 17006110, 18068992, 19131874

Offset: 0

John Mason, Jul 29 2021

The sequence is inspired by the fact that, for any string of decimal digits, s, "almost all" integers contain s in their decimal expansion. (The same is true for other bases.)

			a(1) = 1062880 because exactly half of the integers in [1..1062880] have a 1 in their decimal expansion.

Cf. A343839, A344636, A344474.

Also, this sequence has several values that coincide with values in A117862.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

References

Crossrefs

Programs

Mathematica