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

1,2

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.

Formula

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

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 *)

Prog

(Haskell)
a011531 n = a011531_list !! (n-1)
a011531_list = filter ((elem '1') . show) [0..]
-- Reinhard Zumkeller, Feb 05 2012
(PARI) is_A011531(n)=setsearch(Set(digits(n)), 1) \\ M. F. Hasler, Jan 10 2016
(Magma) [n: n in [0..500] | 1 in Intseq(n) ]; // Vincenzo Librandi, Jan 11 2016
(GAP) Filtered([1..140], n->1 in ListOfDigits(n)); # Muniru A Asiru, Feb 23 2019
(Scala) (0 to 119).filter(_.toString.indexOf('1') > -1) // Alonso del Arte, Jan 12 2020
(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

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).

Sequence in context: A069715 A248499 A008716 * A257946 A070839 A161561

Adjacent sequences: A011528 A011529 A011530 * A011532 A011533 A011534

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Status

approved