A174203 -id:A174203 - cp's OEIS frontend

A174210 In the sequence of nonnegative natural numbers delete every 2nd, 4th, 6th, 8th... occurrence of each individual digit 0, 1, 2,.., 9.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 20, 1, 2, 23, 4, 25, 6, 27, 8, 29, 3, 3, 3, 3, 3, 40, 1, 42, 3, 4, 45, 6, 47, 8, 49, 5, 5, 5, 5, 5, 60, 1, 62, 3, 64, 5, 6, 67, 8, 69, 7, 7, 7, 7, 7, 80, 1, 82, 3, 84, 5, 86, 7, 8, 89, 9, 9, 9, 9, 9, 10, 1, 2, 103, 4, 105, 6, 107, 8, 109, 1, 1, 1, 1, 1, 1

Offset: 0

Paolo P. Lava & Giorgio Balzarotti, Mar 15 2010

			0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29
Delete even occurrences of digit 0 (replaced by ~): 0,1,2,3,4,5,6,7,8,9,1~,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29
Delete even occurrences of digit 1 (replaced by ~): 0,1,2,3,4,5,6,7,8,9,~~,1~,12,~3,14,~5,16,~7,18,~9,20,21,22,23,24,25,26,27,28,29
Delete even occurrences of digit 2 (replaced by ~): 0,1,2,3,4,5,6,7,8,9,~~,1~,1~,~3,14,~5,16,~7,18,~9,20,~1,2~,23,~4,25,~6,27,~8,29
Delete even occurrences of digit 3 (replaced by ~): 0,1,2,3,4,5,6,7,8,9,~~,1~,1~,~~,14,~5,16,~7,18,~9,20,~1,2~,23,~4,25,~6,27,~8,29
Delete even occurrences of digit 4 (replaced by ~): 0,1,2,3,4,5,6,7,8,9,~~,1~,1~,~~,1~,~5,16,~7,18,~9,20,~1,2~,23,~4,25,~6,27,~8,29
Delete even occurrences of digit 5 (replaced by ~): 0,1,2,3,4,5,6,7,8,9,~~,1~,1~,~~,1~,~~,16,~7,18,~9,20,~1,2~,23,~4,25,~6,27,~8,29
Delete even occurrences of digit 6 (replaced by ~): 0,1,2,3,4,5,6,7,8,9,~~,1~,1~,~~,1~,~~,1~,~7,18,~9,20,~1,2~,23,~4,25,~6,27,~8,29
Delete even occurrences of digit 7 (replaced by ~): 0,1,2,3,4,5,6,7,8,9,~~,1~,1~,~~,1~,~~,1~,~~,18,~9,20,~1,2~,23,~4,25,~6,27,~8,29
Delete even occurrences of digit 8 (replaced by ~): 0,1,2,3,4,5,6,7,8,9,~~,1~,1~,~~,1~,~~,1~,~~,1~,~9,20,~1,2~,23,~4,25,~6,27,~8,29
Delete even occurrences of digit 9 (replaced by ~): 0,1,2,3,4,5,6,7,8,9,~~,1~,1~,~~,1~,~~,1~,~~,1~,~~,20,~1,2~,23,~4,25,~6,27,~8,29
Sequence defined by numbers left: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 20, 1, 2, 23, 4, 25, 6, 27, 8, 29,....

Cf. A174203 - A174209.

A174210aux := proc(n) option remember; local f,i,dgs ; if n < 0 then return [seq(0,i=0..9)] ; elif n = 0 then return [1,seq(0,i=1..9)] ; else f := procname(n-1) ; for dgs in convert(n,base,10) do i := op(dgs+1,f) ; f := subsop(dgs+1=i+1,f) ; end do: f ; end if; end proc:
Lton := proc(L,b) add( op(i,L)*b^(i-1),i=1..nops(L)) ; end proc:
A174210 := proc(n) local dgs,f,d; dgs := convert(n,base,10) ; f := A174210aux(n-1) ; for i from nops(dgs) to 1 by -1 do d := op(i,dgs) ; oldd := op(d+1,f) ; if type( 1+oldd,'even') then dgs := subsop(i=NULL,dgs) ; end if; f := subsop(d+1=oldd+1,f) ; end do: d := Lton(dgs,10) ; if d=0 and n>0 then return ; else return d; end if; end proc:
seq(A174210(n),n=0..90) ; # R. J. Mathar, Jun 05 2011

A174205 Write natural numbers in base 2 as a stream of digits. Moving left to right, delete odd occurrences of digit 0 and 1.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1

Offset: 1

Paolo P. Lava and Giorgio Balzarotti, Mar 15 2010

The natural numbers in base 2 are 0, 1, 10, 11, 100, 101, 110, 111, 1000..... and define a stream of digits if concatenated:
0110111001011101111000 Delete odd-indexed occurrences of 0 (replaced by .):
.110111.01.11101111.0. Also delete odd-indexed occurrences of 1 (replaced by .):
..10.1..01..1.01.1..0.
The stream of bits that remain after these two rounds of deletion is chopped into single bits which define the entries of the current sequence.

Cf. A007088, A174203 - A174210.

def A174205(N=100):
    a = [0] + flatten([n.digits(base=2)[::-1] for n in IntegerRange(1,N)])
    for bit in 0, 1:
        a = [d for i,d in enumerate(a) if not (d == bit and a[:i+1].count(bit) % 2 == 1)]
    return a # D. S. McNeil, Dec 08 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

Paolo P. Lava and Giorgio Balzarotti, Mar 15 2010

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, ....

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

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

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 *)

A174204 Scan the sequence of natural numbers, written in base 2, from left to right, delete each 2nd, 4th, 6th etc occurrence of digit 0 and each 2nd, 4th, 6th etc occurrence of digit 1. The sequence are the base-10 residuals.

Original entry on oeis.org

0, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 5, 1, 3, 4, 1, 1, 1, 4, 5, 2, 3, 4, 5, 2, 3, 6, 5, 3, 3, 8

Offset: 0

Paolo P. Lava and Giorgio Balzarotti, Mar 15 2010

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

			Numbers in base 2 (A007088):
0, 1, 10, 11, 100, 101, 110, 111, 1000.....
Delete 2nd, 4th, 6th,.. (even) occurrence of 0 (replaced by ~):
0, 1, 1~, 11, 10~, 101, 11~, 111, 10~0
Delete 2nd, 4th 6th,... (even) occurrence of 1 (replaced by ~):
0, 1, ~~, 1~, 10~, ~01, ~1~, ~1~, 10~0
The numbers left are:
0, 1, 1, 10, 1, 1, 1, 100,  and in base 10: 0, 1, 1, 2, 1, 1, 1, 4, ....as shown by a(n).

Cf. A174203, A174205-A174210.

A174206 Write natural numbers in base 2 as a stream of digits. Moving left to right, delete even occurrences of digit 0 and 1.

Original entry on oeis.org

0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1

Offset: 0

Paolo P. Lava and Giorgio Balzarotti, Mar 15 2010

			Numbers in base 2: 0, 1, 10, 11, 100, 101, 110, 111, 1000..... Stream of digits: 0110111001011101111000 Delete even occurrences of 0(replaced by ~): 011~1110~10111~11110~0 Delete even occurrences of 1(replaced by ~): 01~~1~10~~01~1~~1~10~0 Left digits: 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0,....

A174203-A174205, A174207-A174210

A174208 Write natural numbers in base 2 as a stream of digits. Moving left to right, delete odd occurrences of digit 0 and even occurrences of digit 1.

Original entry on oeis.org

1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1

Offset: 0

Paolo P. Lava and Giorgio Balzarotti, Mar 15 2010

			Numbers in base 2: 0, 1, 10, 11, 100, 101, 110, 111, 1000.....
Stream of digits: 0110111001011101111000...
Delete odd occurrences of 0 (replace by ~): ~110111~01~11101111~0~...
Delete even occurrences of 1 (replace by ~): ~1~01~1~0~~1~10~1~1~0~...
This leaves the digits: 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0,....

Cf. A030190, A174203-A174207, A174209, A174210.

Edited by N. J. A. Sloane, Aug 21 2012

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

Paolo P. Lava & Giorgio Balzarotti, Mar 15 2010

			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,....

Cf. A174203, A174204, A174205, A174206, A174207, A174208, A174210.

cp's OEIS Frontend

A174210 In the sequence of nonnegative natural numbers delete every 2nd, 4th, 6th, 8th... occurrence of each individual digit 0, 1, 2,.., 9.

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Maple

A174205 Write natural numbers in base 2 as a stream of digits. Moving left to right, delete odd occurrences of digit 0 and 1.

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Sage

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

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Mathematica

A174204 Scan the sequence of natural numbers, written in base 2, from left to right, delete each 2nd, 4th, 6th etc occurrence of digit 0 and each 2nd, 4th, 6th etc occurrence of digit 1. The sequence are the base-10 residuals.

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A174206 Write natural numbers in base 2 as a stream of digits. Moving left to right, delete even occurrences of digit 0 and 1.

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A174208 Write natural numbers in base 2 as a stream of digits. Moving left to right, delete odd occurrences of digit 0 and even occurrences of digit 1.

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Extensions

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

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