

A344636


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


4



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

1,2


COMMENTS

Andrew Hilton (see Ref) refers to these as "halfone" numbers.


REFERENCES

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


LINKS



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



KEYWORD

nonn,base,fini,full


AUTHOR



STATUS

approved



