A011531 Numbers that contain a digit 1 in their decimal representation.

1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Comments

A121042(a(n)) = 1. - Reinhard Zumkeller, Jul 21 2006

See A043493 for numbers that contain a single digit '1'. A subsequence of numbers having a digit that divides all other digits, A263314. - M. F. Hasler, Jan 11 2016

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A121041, A121022, A121023, A121024, A121025, A121026, A121027, A121028, A121029, A121030, A121031, A121032, A121033, A121034, A121035, A121036, A121037, A121038, A121039, A121040.

Cf. A052383 (complement), A062634 (a subsequence).

Programs

GAP

Filtered([1..140],n->1 in ListOfDigits(n)); # Muniru A Asiru, Feb 23 2019

Haskell

a011531 n = a011531_list !! (n-1)
a011531_list = filter ((elem '1') . show) [0..]
-- Reinhard Zumkeller, Feb 05 2012

Magma

[n: n in [0..500] | 1 in Intseq(n) ]; // Vincenzo Librandi, Jan 11 2016

Maple

M:= 3: # to get all terms of up to M digits
B:= {1}: A:= {1}:
for i from 2 to M do
   B:= map(t -> seq(10*t+j,j=0..9),B) union
      {seq(10*x+1,x=2*10^(i-2)..10^(i-1)-1)}:
   A:= A union B;
od:
sort(convert(A,list)); # Robert Israel, Jan 10 2016
# second program:
A011531 := proc(n)
    if n = 1 then
        1;
    else
        for a from procname(n-1)+1 do
            if nops(convert(convert(a,base,10),set) intersect {1}) > 0 then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Jul 31 2016

Mathematica

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

PARI

is_A011531(n)=setsearch(Set(digits(n)),1) \\ M. F. Hasler, Jan 10 2016

Python

def aupto(nn): return [m for m in range(1, nn+1) if '1' in str(m)]
print(aupto(133)) # Michael S. Branicky, Jan 10 2021

Scala

(0 to 119).filter(.toString.indexOf('1') > -1) // _Alonso del Arte, Jan 12 2020

Formula

a(n) ~ n. - Charles R Greathouse IV, Nov 02 2022