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.

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

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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

A174207 Depleted stream of the natural numbers written in base 2: delete even occurrences of digit 0 and odd occurrences of digit 1.

Original entry on oeis.org

0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0
Offset: 0

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Mar 15 2010

Keywords

Comments

The numbers in base 2: 0, 1, 10, 11, 100, 101, 110, 111, 1000, ....
The infinite stream of digits: 0110111001011101111000...
Delete even (2nd, 4th, 6th, ...) occurrences of 0 (replaced by ~):
011~1110~10111~11110~0...
Delete odd (1st, 3rd, 5th, ...) occurrences of 1 (replaced by ~):
0~1~~1~0~10~1~~1~1~0~0...
Digits remaining define the sequence: 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, ....

Crossrefs

Cf. A174203, A174204 (base 10), A174205, A174206, A174208-A174210.

Programs

  • Maple
    nb := 100 ;
L := [0] ;
for n from 1 to nb do
    nn := ListTools[Reverse](convert(n,base,2)) ;
    L := [op(L),op(nn)] ;
end do;
Lout := [] ;
ie :=1 ;
io :=1 ;
for i from 1 to nops(L) do
    if op(i,L) =0 then
        if ie>0 then
            if type(ie,'odd') then
                printf("%d,",0) ;
            end if;
        end if;
        ie := ie+1 ;
    else
        if io>0 then
            if type(io,'even') then
                printf("%d,",1) ;
            end if;
        end if;
        io := io+1 ;
    end if;
end do: # R. J. Mathar, Dec 06 2011
  • Mathematica
    nMax = 60; bits = Join @@ Table[IntegerDigits[n, 2], {n, 0, nMax}]; pos0 = Position[bits, 0] // Flatten; even0 = Partition[pos0, 2][[All, 2]]; bits2 = ReplacePart[bits, Alternatives @@ even0 -> "~"]; pos1 = Position[bits2, 1] // Flatten; odd1 = Partition[pos1, 2][[All, 1]]; DeleteCases[ ReplacePart[ bits2, Alternatives @@ odd1 -> "~"], "~"] (* Jean-François Alcover, Nov 18 2016 *)

A174209 In the sequence of natural numbers, moving left to right, delete 1st, 3rd, 5th, 7th etc occurrence of each of the ten digits.

Original entry on oeis.org

10, 1, 2, 13, 4, 15, 6, 17, 8, 19, 2, 2, 2, 2, 2, 30, 1, 32, 3, 4, 35, 6, 37, 8, 39, 4, 4, 4, 4, 4, 50, 1, 52, 3, 54, 5, 6, 57, 8, 59, 6, 6, 6, 6, 6, 70, 1, 72, 3, 74, 5, 76, 7, 8, 79, 8, 8, 8, 8, 8, 90, 1, 92, 3, 94, 5, 96, 7, 98, 9, 0, 10, 1, 0, 1, 0, 1, 0, 1, 0, 1, 11, 12, 13, 14, 15, 16, 17
Offset: 0

Views

Author

Paolo P. Lava & Giorgio Balzarotti, Mar 15 2010

Keywords

Examples

			Starting from
0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,20,21,22,23,24,25,26,27,28,29,..
Delete odd occurrences of digit 0 (replaced by ~):
,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,2~,21,22,23,24,25,26,27,28,29,..
Delete odd occurrences of digit 1 (replaced by ~):
,~,2,3,4,5,6,7,8,9,10,~1,~2,13,~4,15,~6,17,~8,19,2~,2~,22,23,24,25,26,27,28,29 ,..
Delete odd occurrences of digit 2 (replaced by ~):
,~,~,3,4,5,6,7,8,9,10,~1,~2,13,~4,15,~6,17,~8,19,~~,2~,~2,~3,24,~5,26,~7,28,~9 ,..
Delete odd occurrences of digit 3 (replaced by ~):
,~,~,~,4,5,6,7,8,9,10,~1,~2,13,~4,15,~6,17,~8,19,~~,2~,~2,~~,24,~5,26,~7,28,~9,..
Delete odd occurrences of digit 4 (replaced by ~):
,~,~,~,~,5,6,7,8,9,10,~1,~2,13,~4,15,~6,17,~8,19,~~,2~,~2,~~,2~,~5,26,~7,28,~9,..
Delete odd occurrences of digit 5 (replaced by ~):
,~,~,~,~,~,6,7,8,9,10,~1,~2,13,~4,15,~6,17,~8,19,~~,2~,~2,~~,2~,~~,26,~7,28,~9,..
Delete odd occurrences of digit 6 (replaced by ~):
,~,~,~,~,~,~,7,8,9,10,~1,~2,13,~4,15,~6,17,~8,19,~~,2~,~2,~~,2~,~~,2~,~7,28,~9,..
Delete odd occurrences of digit 7 (replaced by ~):
,~,~,~,~,~,~,~,8,9,10,~1,~2,13,~4,15,~6,17,~8,19,~~,2~,~2,~~,2~,~~,2~,~~,28,~9,..
Delete odd occurrences of digit 8 (replaced by ~):
,~,~,~,~,~,~,~,~,9,10,~1,~2,13,~4,15,~6,17,~8,19,~~,2~,~2,~~,2~,~~,2~,~~,2~,~9,..
Delete odd occurrences of digit 9 (replaced by ~):
,~,~,~,~,~,~,~,~,~,10,~1,~2,13,~4,15,~6,17,~8,19,~~,2~,~2,~~,2~,~~,2~,~~,2~,~~,..
The residual digits define the sequence: 10, 1, 2, 13, 4, 15, 6, 17, 8, 19, 2, 2, 2, 2, 2,....

Crossrefs

Cf. A174203, A174204, A174205, A174206, A174207, A174208, A174210.
Showing 1-3 of 3 results.

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