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

Author

Paolo P. Lava & Giorgio Balzarotti, Mar 15 2010

Keywords

• nonn
• easy
• base

Examples

			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,....
		

Crossrefs

Cf. A174203 - A174209.

Programs

Maple

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