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A268609 Record values in A004290.

%I A268609 #35 Aug 02 2025 14:50:45
%S A268609 1,10,111,1110,111111111,1111111110,11111111100,111111111000,
%T A268609 111111111111111111,1111111111111111110,11111111111111111100,
%U A268609 111111111111111111000,111111111111111111111111111,1111111111111111111111111110,11111111111111111111111111100,111111111111111111111111111000
%N A268609 Record values in A004290.
%C A268609 a(18) is the first term that is neither a repunit nor the product of a repunit and a power of 10.
%H A268609 David Radcliffe, <a href="/A268609/b268609.txt">Table of n, a(n) for n = 1..28</a>
%e A268609 1110 is a term because A004290(6) = 1110 and A004290(n) < 1110 for all n < 6, where A004290(n) is the least positive multiple of n that when written in base 10 uses only 0's and 1's.
%p A268609 A004290:= proc(n)
%p A268609 local L,x,m,r,k,j;
%p A268609 for x from 2 to n-1 do L[0,x]:= 0 od:
%p A268609 L[0,0]:= 1: L[0,1]:= 1;
%p A268609 for m from 1 do
%p A268609    if L[m-1,(-10^m) mod n] = 1 then break fi;
%p A268609    L[m,0]:= 1;
%p A268609    for k from 1 to n-1 do
%p A268609      L[m,k]:= max(L[m-1,k],L[m-1,k-10^m mod n])
%p A268609    od;
%p A268609 od;
%p A268609 r:= 10^m; k:= -10^m mod n;
%p A268609 for j from m-1 by -1 to 1 do
%p A268609     if L[j-1,k] = 0 then
%p A268609       r:= r + 10^j; k:= k - 10^j mod n;
%p A268609     fi
%p A268609 od;
%p A268609 if k = 1 then r:= r + 1 fi;
%p A268609 r
%p A268609 end proc:
%p A268609 A004290(1):= 1:
%p A268609 count:= 0: m:= 0;
%p A268609 for n from 1 to 20000 do
%p A268609   v:= A004290(n);
%p A268609   if v > m then
%p A268609     count:= count+1;
%p A268609     A[count]:= v;
%p A268609     m:= v;
%p A268609   fi
%p A268609 od:
%p A268609 seq(A[i],i=1..count); # _Robert Israel_, Feb 09 2016
%Y A268609 Cf. A004290, A268610. Subsequence of A007088.
%K A268609 nonn,base
%O A268609 1,2
%A A268609 _David Radcliffe_, Feb 08 2016
%E A268609 a(1)=0 prepended to terms, b-file and Maple by _Georg Fischer_, Jun 24 2020
%E A268609 Initial 0 removed for consistency with change in A004290 by _Sean A. Irvine_, Feb 19 2024