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 1-10 of 784 results. Next

A099821 Odd positive integers in base 2 (bisection of A007088).

Original entry on oeis.org

1, 11, 101, 111, 1001, 1011, 1101, 1111, 10001, 10011, 10101, 10111, 11001, 11011, 11101, 11111, 100001, 100011, 100101, 100111, 101001, 101011, 101101, 101111, 110001, 110011, 110101, 110111, 111001, 111011, 111101, 111111, 1000001
Offset: 1

Views

Author

N. J. A. Sloane, Nov 19 2004

Keywords

Comments

List of binary vectors that begin and end with 1.

Links

Crossrefs

Cf. A007088, A099820.

Programs

  • Maple
    seq(convert(2*n-1,binary),n=1..37); # Emeric Deutsch, Dec 15 2004
  • Mathematica
    FromDigits/@IntegerDigits[Range[1,71,2],2] (* Harvey P. Dale, Apr 05 2019 *)
  • PARI
    a(n) = fromdigits(binary(2*n-1), 10); \\ Michel Marcus, Apr 23 2020

Extensions

More terms from Emeric Deutsch, Dec 15 2004

A122230 a(n) = A007088(A122229(n)).

Original entry on oeis.org

0, 10, 1100, 111000, 11100100, 1110011000, 111001100100, 11100110011000, 1110011001100100, 111001100110011000, 11100110011001100100, 1110011001100110011000, 111001100110011001100100
Offset: 0

Views

Author

Antti Karttunen, Sep 14 2006

Keywords

Crossrefs

Cf. A080070, A122233, A122236, A122240, A122243, A122246.

A122233 a(n) = A007088(A122232(n)).

Original entry on oeis.org

101010, 11010100, 1111100000, 111100100100, 11110001011000, 1111110010000100, 111101100010011000, 11110001101100100100, 1111101011000110000100, 111101100110001100010100
Offset: 1

Views

Author

Antti Karttunen, Sep 14 2006

Keywords

Crossrefs

Cf. A080070, A122230, A122236, A122240, A122243, A122246.

A122243 a(n) = A007088(A122242(n)).

Original entry on oeis.org

101010, 11110000, 1110010100, 111010100100, 11101001110000, 1111001010011000, 111100100101110000, 11101100101001011000, 1110110010011011100000, 111100111001000110110000
Offset: 1

Views

Author

Antti Karttunen, Sep 14 2006

Keywords

Crossrefs

A080070, A122230, A122233, A122236, A122240, A122246.

A122246 a(n) = A007088(A122245(n)).

Original entry on oeis.org

101100, 11101000, 1110011000, 111100100100, 11101001011000, 1110110010011000, 111100100110110000, 11110011010001011000, 1110110010010110101000, 111011001110000110110000
Offset: 1

Views

Author

Antti Karttunen, Sep 14 2006

Keywords

Crossrefs

A080070, A122230, A122233, A122236, A122240, A122243.

A174203 In the sequence A007088 of binary representations of n, delete the 1st, 3rd, 5th, 7th, 9th etc occurrence of 0 and 1. Rewrite the bits left over in base 10.

Original entry on oeis.org

2, 1, 0, 1, 2, 3, 0, 2, 2, 5, 2, 1, 6, 3, 0, 2, 4, 5, 2, 1, 5, 3, 2, 2, 5, 5, 2, 3, 6, 7, 0, 4, 4, 9, 2, 1, 10, 3, 4, 2, 10, 5, 2, 5, 5, 11, 4, 2, 10, 5, 2, 5, 5, 11, 2, 6, 6, 13, 6, 3, 14, 7, 0, 4, 8, 9, 2, 1, 9, 3, 2, 2, 9, 5, 2, 5, 10, 11, 4
Offset: 0

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Mar 15 2010

Keywords

Comments

Deleting the odd occurrences of 0 and the even occurrences of 1, we get the same sequence apart from the initial 2 replaced by 1 and 0.

Examples

			Numbers in base 2: 0, 1, 10, 11, 100, 101, 110, 111, 1000, .... Delete odd occurrences of 0 (replaced by ~): ~, 1, 10, 11, 1~0, 1~1, 110, 111, 1~0~ Delete odd occurrences of 1 (replaced by ~): ~, ~, 10, ~1, ~~0, 1~~, 1~0, 1~1, ~~0~.
The pieces left are 10, 1, 0, 1, 10, 11, 0, ... which is in base 10: 2, 1, 0, 1, 2, 3, 0, ....

Crossrefs

Cf. A174204, A174205, A174206, A174207, A174208, A174209, A174210.

Programs

  • Maple
    n1 := 1 ; n0 := 1 ;
for n from 0 to 80 do
        if n = 0 then b := [0] ; else b := convert(n,base,2) ; end if;
        for d from nops(b) to 1 by -1 do
                if op(d,b) = 0 then
                        if type(n0,'odd') then b := subsop(d=NULL,b) ; end if; n0 := n0+1 ;
                else
                        if type(n1,'odd') then b := subsop(d=NULL,b) ; end if; n1 := n1+1 ;
                end if;
        end do:
        add(2^(i-1)*op(i,b),i=1..nops(b)) ; printf("%d,",%) ;
end do: # R. J. Mathar, Nov 23 2010

Extensions

Sequence extended, keyword:base,less added by R. J. Mathar, Nov 23 2010

A122236 a(n) = A007088(A122235(n)).

Original entry on oeis.org

101100, 11011000, 1111001000, 111100010100, 11111100000100, 1111001001110000, 111100010111000100, 11111111000010000100, 1111100010011011000100, 111101101001110000100100
Offset: 1

Views

Author

Antti Karttunen, Sep 14 2006

Keywords

Crossrefs

Cf. A080070, A122230, A122233, A122240, A122243, A122246.

A122240 a(n) = A007088(A122239(n)).

Original entry on oeis.org

110100, 11110000, 1111000100, 111110000100, 11110011000100, 1111110000010100, 111100100111100000, 11110001011100100100, 1111111000101100000100, 111100101001101001110000
Offset: 1

Views

Author

Antti Karttunen, Sep 14 2006

Keywords

Crossrefs

Cf. A080070, A122230, A122233, A122236, A122243, A122246.

A080317 a(n) = A007088(A080316(n)).

Original entry on oeis.org

0, 1100, 11001100, 11110000, 110011001100, 110011110000, 111111000000, 111100001100, 111100110000, 1100110011001100, 1100110011110000, 1100111111000000, 1100111100001100, 1100111100110000, 1111110000001100
Offset: 0

Views

Author

Antti Karttunen, Mar 02 2003

Keywords

Comments

Note that here we have totally balanced binary sequences (as in A014486/A063171), 10, 1010, 1100, 101010, 101100, 110010, ..., but with each bit duplicated. Furthermore, the order is a bit different.

A099820 Even nonnegative integers in base 2 (bisection of A007088).

Original entry on oeis.org

0, 10, 100, 110, 1000, 1010, 1100, 1110, 10000, 10010, 10100, 10110, 11000, 11010, 11100, 11110, 100000, 100010, 100100, 100110, 101000, 101010, 101100, 101110, 110000, 110010, 110100, 110110, 111000, 111010, 111100, 111110, 1000000
Offset: 0

Views

Author

N. J. A. Sloane, Nov 19 2004

Keywords

Links

Crossrefs

Cf. A007088, A099821.

Programs

  • Maple
    seq(convert(2*n,binary),n=0..37); # Emeric Deutsch, Dec 15 2004

Extensions

More terms from Emeric Deutsch, Dec 15 2004
Showing 1-10 of 784 results. Next

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

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