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

0,3

Links

Table of n, a(n) for n=0..90.

Example

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,....

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

Crossrefs

Cf. A174203 - A174209.

Sequence in context: A179635 A306354 A216587 * A134777 A253015 A257295

Adjacent sequences: A174207 A174208 A174209 * A174211 A174212 A174213

Keyword

nonn,easy,base

Author

Paolo P. Lava & Giorgio Balzarotti, Mar 15 2010

Status

approved