cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

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

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

A267086 Numbers such that the number formed by digits in even positions divides, or is divisible by, the number formed by the digits in odd positions; zero allowed.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 30, 31, 33, 36, 39, 40, 41, 42, 44, 48, 50, 51, 55, 60, 61, 62, 63, 66, 70, 71, 77, 80, 81, 82, 84, 88, 90, 91, 93, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 122, 124, 126, 128, 132, 135
Offset: 1

Views

Author

M. F. Hasler, Jan 10 2016

Keywords

Comments

The initial 0 is included by convention. The single-digit numbers are included with the reasoning that the number formed by digits in even positions is zero, and thus divisible by (= a multiple of) any other number, and here in particular the number formed by first digit.
By "digits in odd positions" we mean the first (most significant), third, fifth, etc. digits; e.g., for the numbers 12345 or 123456 this would be 135.
An extended version of Eric Angelini's "integears" A267085.
Sequence A263314 is a subsequence up to 120, but 121 is in A263314 and not in this sequence.

Examples

			12 is in the sequence because 1 divides 2.
213 is in the sequence because 1 divides 23.
1020 is in the sequence because 12 divides 00 = 0. (Any number divides 0 therefore any number which has every other digit equal to zero is in the sequence.)

Links

Crossrefs

Cf. A267085, A263314.
See also A080463, A080464 and A080465.

Programs

A263315 Numbers whose decimal representation contains at least two digits such that no digit is divisible by any other digit.

Original entry on oeis.org

23, 25, 27, 29, 32, 34, 35, 37, 38, 43, 45, 46, 47, 49, 52, 53, 54, 56, 57, 58, 59, 64, 65, 67, 68, 69, 72, 73, 74, 75, 76, 78, 79, 83, 85, 86, 87, 89, 92, 94, 95, 96, 97, 98, 235, 237, 253, 257, 259, 273, 275, 279, 295, 297, 325, 327, 345, 347, 352, 354, 357
Offset: 1

Views

Author

Giovanni Teofilatto, Oct 14 2015

Keywords

Comments

This sequence is finite. Digits 0 or 1 do not occur.
Digits must be mutually coprime and thus none can be repeated. The number 1 is coprime to all numbers thus it is left out of consideration. - Michael De Vlieger, Mar 25 2017

Examples

			From _Michael De Vlieger_, Mar 25 2017: (Start)
29 is in the sequence because the digits 2 and 9 are coprime and not equal to 1.
325 is in the sequence because digits 3, 2, and 5 are mutually coprime and none are equal to 1. (End)

Links

Crossrefs

Cf. A263314.

Programs

  • Mathematica
    Select[Range@ 360, CoprimeQ @@ # && ! MemberQ[#, 1] &@ IntegerDigits@ # &] (* Michael De Vlieger, Mar 25 2017 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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