A011533 Numbers that contain a 3.

3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93, 103, 113, 123, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 143, 153, 163, 173, 183, 193, 203, 213, 223, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 243, 253

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• James Grime and Brady Haran, 3 is everywhere, Numberphile video, 2012.
• Index entries for 10-automatic sequences.

Crossrefs

Complement: A052405.

Cf. A016189.

Numbers that contain a digit k: A011531 (k=1), A011532 (k=2), A011534 (k=4), A011535 (k=5), A011536 (k=6), A011537 (k=7), A011538 (k=8), A011539 (k=9), A011540 (k=0).

Programs

GAP

Filtered([1..260],n->3 in ListOfDigits(n)); # Muniru A Asiru, Feb 23 2019

Haskell

a011533 n = a011533_list !! (n-1)
a011533_list = filter ((elem '3') . show) [0..]
-- Reinhard Zumkeller, Apr 10 2015

Magma

[n: n in [0..500] | 3 in Intseq(n)]; // Vincenzo Librandi, Jan 11 2016

Maple

M:= 3: # to get all terms of up to M digits
B:= {3}: A:= {3}:
for i from 2 to M do
   B:= map(t -> seq(10*t+j,j=0..9),B) union
      {seq(10*x+3,x=10^(i-2)..10^(i-1)-1)}:
   A:= A union B;
od:
sort(convert(A,list));# Robert Israel, Jan 11 2016

Mathematica

Select[Range[600] - 1, DigitCount[#, 10, 3]>0 &] (* Vincenzo Librandi, Jan 11 2016 *)

PARI

isok(n)=my(d=digits(n)); for (k=1, #d, if (d[k] == 3, return (1))); \\ Michel Marcus, Jan 11 2016

Formula

a(n) ~ n. - Charles R Greathouse IV, Aug 28 2012

For m >= 1, a(10^m - 9^m) = 10^m-7, a(10^m - 9^m + 1) = 10^m + 3. - Robert Israel, Jan 11 2016