A108199 - OEIS

%I #22 Mar 05 2024 15:02:57

%S 2,11,12,13,14,15,16,17,18,19,21,23,25,27,29,32,35,38,42,46,51,56,62,

%T 68,75,83,92,102,103,104,105,106,107,108,109,110,111,112,113,114,115,

%U 116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132

%N a(n) contains the digits of the remainder of a(n)/a(n-1). Sequence starts with 2.

%C Clarifications: To reproduce the terms, only a(n) > a(n-1) are admitted. If the remainder is zero, that candidate a(n) is not admitted and the next larger a(n) is tested. (See the Maple implementation). Example: after 2, the candidates 3 to 9 are not admitted (remainder's digits are not subsets of candidate digits), but 10 (remainder 0) is also not admitted; finally 11 (remainder 11/2=1) follows 2. - _R. J. Mathar_, Feb 23 2024

%H Alois P. Heinz, <a href="/A108199/b108199.txt">Table of n, a(n) for n = 1..20000</a>

%e 11 divided by 2 is 5 + remainder 1; "1" is in "11".

%e 12 divided by 11 is 1 + remainder 1; "1" is in "12".

%p A108199 := proc(n)

%p     option remember ;

%p     local a,r,dgsa,dgsr ;

%p     if n =1 then

%p         2;

%p     else

%p         for a from procname(n-1)+1 do

%p             r := modp(a,procname(n-1)) ;

%p             if r > 0 then

%p                 dgsa := convert(a,base,10) ;

%p                 dgsr := convert(r,base,10) ;

%p                 if verify(dgsr,dgsa,'sublist') then

%p                     return a;

%p                 end if;

%p             end if;

%p         end do:

%p     end if;

%p end proc:

%p seq(A108199(n),n=1..60) ; # _R. J. Mathar_, Jun 20 2021

%p # second Maple program:

%p d:= n-> {convert(n, base, 10)[]}:

%p a:= proc(n) option remember; local k; for k from 1+a(n-1) while

%p      (r-> r=0 or d(r) minus d(k)<>{})(irem(k, a(n-1))) do od; k

%p     end: a(1):=2:

%p seq(a(n), n=1..60);  # _Alois P. Heinz_, Mar 05 2024

%t l={2};a[1]=2;k=2;Do[r=Mod[n,a[k-1]];If[ContainsAny[IntegerDigits[r],IntegerDigits[n]],If[r>0,AppendTo[l,n];a[k]=n;k++]],{n,3,127}];l (* _James C. McMahon_, Feb 25 2024 *)

%K base,easy,nonn

%O 1,1

%A _Eric Angelini_, Jun 15 2005

%E Offset set to 1 by _R. J. Mathar_, Jun 20 2021