|
%I #12 Aug 11 2015 09:17:08
%S 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,
%T 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,
%U 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
%N In the sequence of nonnegative natural numbers delete every 2nd, 4th, 6th, 8th... occurrence of each individual digit 0, 1, 2,.., 9.
%e 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
%e 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
%e 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
%e 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
%e 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
%e 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
%e 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
%e 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
%e 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
%e 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
%e 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
%e 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,....
%p 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:
%p Lton := proc(L,b) add( op(i,L)*b^(i-1),i=1..nops(L)) ; end proc:
%p 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:
%p seq(A174210(n),n=0..90) ; # _R. J. Mathar_, Jun 05 2011
%Y Cf. A174203 - A174209.
%K nonn,easy,base
%O 0,3
%A _Paolo P. Lava_ & _Giorgio Balzarotti_, Mar 15 2010
|
