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 1-6 of 6 results.

A004753 Numbers whose binary expansion contains 100.

Original entry on oeis.org

4, 8, 9, 12, 16, 17, 18, 19, 20, 24, 25, 28, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 44, 48, 49, 50, 51, 52, 56, 57, 60, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 88, 89, 92, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Complement of A003754.
Subsequence of A247875.
Cf. A004748, A004749, A004750, A004752.

Programs

  • Haskell
    a004753 n = a004753_list !! (n-1)
a004753_list = filter f [0..] where
   f 0 = False; f x = x `mod` 4 == 0 || f (x `div` 2)
-- Reinhard Zumkeller, Oct 27 2011
  • Mathematica
    Select[Range[110],MemberQ[Partition[IntegerDigits[#,2],3,1],{1,0,0}]&] (* Harvey P. Dale, Mar 14 2014 *)
  • PARI
    is(n)=n=binary(n);for(i=3,#n,if(n[i-2]&&!n[i]&&!n[i-1],return(1)));0 \\ Charles R Greathouse IV, Sep 24 2012
  • PARI
    is(n)=while(n>3, if(bitand(n,7)==4, return(1)); n>>=1); 0 \\ Charles R Greathouse IV, Feb 11 2017

Formula

a(n) ~ n. - Charles R Greathouse IV, Sep 24 2012

A004749 Numbers whose binary expansion contains the substring '110'.

Original entry on oeis.org

6, 12, 13, 14, 22, 24, 25, 26, 27, 28, 29, 30, 38, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 70, 76, 77, 78, 86, 88, 89, 90, 91, 92, 93, 94, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			22 is in the sequence because 22 = 10110_2 and '10110' has '110' as one of its substrings. - _Indranil Ghosh_, Feb 11 2017

Links

Crossrefs

Cf. A004748, A004750, A004751, A004752, A004753.

Programs

  • Mathematica
    Select[Range[200],SequenceCount[IntegerDigits[#,2],{1,1,0}]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 07 2017 *)
  • PARI
    is(n)=while(n>5,if(bitand(n,7)==6, return(1)); n>>=1); 0 \\ Charles R Greathouse IV, Feb 11 2017
  • Python
    i=j=0
while j<=500:
    if "110" in bin(i)[2:]:
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Feb 11 2017

Formula

a(n) ~ n. - Charles R Greathouse IV, Oct 23 2015

Extensions

Offset corrected by Charles R Greathouse IV, Feb 11 2017

A004752 Binary expansion contains 010.

Original entry on oeis.org

10, 18, 20, 21, 26, 34, 36, 37, 40, 41, 42, 43, 50, 52, 53, 58, 66, 68, 69, 72, 73, 74, 75, 80, 81, 82, 83, 84, 85, 86, 87, 90, 98, 100, 101, 104, 105, 106, 107, 114, 116, 117, 122, 130, 132, 133, 136, 137, 138, 139, 144, 145, 146, 147, 148, 149, 150
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			20 is in the sequence because, 20 = 10100_2 and '10100' has '010' as one of its substrings. - _Indranil Ghosh_, Feb 11 2017

Links

Crossrefs

Cf. A004748, A004749, A004750, A004751, A004753.

Programs

  • Mathematica
    Select[Range@ 150, Length@ SequencePosition[IntegerDigits[#, 2], {0, 1, 0}] > 0 &] (* Version 10.1, or *)
Select[Range@ 150, MemberQ[Partition[IntegerDigits[#, 2], 3, 1], {0, 1, 0}] &] (* Michael De Vlieger, Feb 11 2017 *)
  • PARI
    is(n)=while(n>9, if(bitand(n, 7)==2, return(1)); n>>=1); 0 \\ Charles R Greathouse IV, Feb 11 2017
  • Python
    i=j=0
while j<=100:
    if "010" in bin(i)[2:]:
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Feb 11 2017

Formula

a(n) ~ n. - Charles R Greathouse IV, Oct 23 2015

Extensions

Offset corrected by Charles R Greathouse IV, Feb 11 2017

A004751 Binary expansion contains 001.

Original entry on oeis.org

9, 17, 18, 19, 25, 33, 34, 35, 36, 37, 38, 39, 41, 49, 50, 51, 57, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 89, 97, 98, 99, 100, 101, 102, 103, 105, 113, 114, 115, 121, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			19 is in the sequence because 19 = 10011_2 and '10011' has '001' as one of its substrings. - _Indranil Ghosh_, Feb 11 2017

Links

Crossrefs

Cf. A004748, A004749, A004750, A004752, A004753.

Programs

  • Mathematica
    Select[Range@ 139, Length@ SequencePosition[IntegerDigits[#, 2], {0, 0, 1}] > 0 &] (* Version 10.1, or *)
Select[Range@ 139, MemberQ[Partition[IntegerDigits[#, 2], 3, 1], {0, 0, 1}] &] (* Michael De Vlieger, Feb 11 2017 *)
Select[Range[150],SequenceCount[IntegerDigits[#,2],{0,0,1}]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 15 2018 *)
  • PARI
    is(n)=while(n>8, if(bitand(n,7)==1, return(1)); n>>=1); 0 \\ Charles R Greathouse IV, Feb 11 2017
  • Python
    i=j=0
while j<=100:
    if "001" in bin(i)[2:]:
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Feb 11 2017

Formula

a(n) ~ n. - Charles R Greathouse IV, Oct 23 2015

Extensions

Offset corrected by Charles R Greathouse IV, Feb 11 2017

A377167 Nonnegative integers containing isolated zeros in their binary representation.

Original entry on oeis.org

0, 2, 5, 6, 10, 11, 13, 14, 18, 20, 21, 22, 23, 26, 27, 29, 30, 34, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 50, 52, 53, 54, 55, 58, 59, 61, 62, 66, 69, 70, 74, 75, 77, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 98, 101, 102, 104, 105, 106
Offset: 1

Views

Author

Paolo Xausa, Oct 18 2024

Keywords

Comments

A 0 is isolated if it's not adjacent to another 0.

Examples

			18 is a term because 18 = 10010_2 contains one isolated 0.
85 is a term because all zeros in 85 = 1010101_2 are isolated.

Links

Crossrefs

Complement of A175054.
Cf. A004748, A007088, A377169.

Programs

  • Mathematica
    Select[Range[0, 150], MemberQ[Split[IntegerDigits[#, 2]], {0}] &]

Formula

{ k : k=0 or 2k+1 in {A004748} }.

A300302 Square array T(n, k) (n >= 1, k >= 1) read by antidiagonals upwards: T(n, k) is the k-th positive number whose binary representation contains the binary representation of n as a substring.

Original entry on oeis.org

1, 2, 2, 3, 4, 3, 4, 6, 5, 4, 5, 8, 7, 6, 5, 6, 10, 9, 11, 8, 6, 7, 12, 11, 12, 12, 9, 7, 8, 14, 13, 13, 16, 13, 10, 8, 9, 16, 15, 14, 20, 17, 14, 11, 9, 10, 18, 17, 23, 22, 21, 18, 15, 12, 10, 11, 20, 19, 24, 28, 24, 22, 19, 19, 13, 11, 12, 22, 21, 25, 32, 29
Offset: 1

Views

Author

Rémy Sigrist, Mar 08 2018

Keywords

Comments

Each positive number k appears A122953(k) times in this array.

Examples

			Square array begins:
  n\k|    1    2    3    4    5    6    7    8    9   10
  ---+--------------------------------------------------
    1|    1    2    3    4    5    6    7    8    9   10  <--  A000027
    2|    2    4    5    6    8    9   10   11   12   13  <--  A062289
    3|    3    6    7   11   12   13   14   15   19   22  <--  A004780
    4|    4    8    9   12   16   17   18   19   20   24  <--  A004753
    5|    5   10   11   13   20   21   22   23   26   27  <--  A004748
    6|    6   12   13   14   22   24   25   26   27   28  <--  A004749
    7|    7   14   15   23   28   29   30   31   39   46  <--  A004781
    8|    8   16   17   24   32   33   34   35   40   48  <--  A004779
    9|    9   18   19   25   36   37   38   39   41   50
   10|   10   20   21   26   40   41   42   43   52   53  <--  A132782

Links

Crossrefs

Cf. A000027, A004748, A004749, A004753, A004779, A004780, A004781, A062289, A122953, A132782.

Programs

  • Perl
    See Links section.

Formula

T(n, 1) = n.
T(n, 2) = 2*n.
T(n, 3) = 2*n + 1.
T(1, n) = A000027(n).
T(2, n) = A062289(n).
T(3, n) = A004780(n).
T(4, n) = A004753(n).
T(5, n) = A004748(n).
T(6, n) = A004749(n).
T(7, n) = A004781(n).
T(8, n) = A004779(n-1).
T(10, n) = A132782(n).
Showing 1-6 of 6 results.

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

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