A039127 Numbers whose base-10 representation has the same number of 1's and 9's.

0, 2, 3, 4, 5, 6, 7, 8, 19, 20, 22, 23, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 37, 38, 40, 42, 43, 44, 45, 46, 47, 48, 50, 52, 53, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 67, 68, 70, 72, 73, 74, 75, 76, 77, 78, 80, 82, 83, 84, 85, 86, 87, 88, 91, 109, 129, 139

Offset

1,2

Comments

A k-digit number is in the sequence with probability ~ 1/sqrt(2*Pi*k/5). - Charles R Greathouse IV, Feb 19 2014

The number of d-digits positive terms is given by 7*8^(d-1)+ 7*sum(k=1,..,floor((d-1)/2), 8^(d-1-2*k) (k, k, d-1-2*k)!) + 2*sum(k=1,..,floor(d/2), 8^(d-2*k) (k, k-1, d-2*k)!), where (x,y,z)! = (x+y+z)!/(x! y! z!) denotes a multinomial coefficient. (* Giovanni Resta, Feb 22 2014 *)

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1500

Mathematica

Select[Range[0, 200], DigitCount[#, 10, 1]==DigitCount[#, 10, 9]&] (* Harvey P. Dale, Feb 19 2014 *)

Prog

(PARI) is(n)=my(v=digits(n)); sum(i=1, #v, if(v[i]==1, 1, if(v[i]==9, -1, 0)))==0 \\ Charles R Greathouse IV, Feb 19 2014

Crossrefs

Sequence in context: A173577 A103205 A363490 * A024650 A037343 A366947

Adjacent sequences: A039124 A039125 A039126 * A039128 A039129 A039130

Keyword

nonn,base,easy

Author

Olivier Gérard

Status

approved