A268609 Record values in A004290.

1, 10, 111, 1110, 111111111, 1111111110, 11111111100, 111111111000, 111111111111111111, 1111111111111111110, 11111111111111111100, 111111111111111111000, 111111111111111111111111111, 1111111111111111111111111110, 11111111111111111111111111100, 111111111111111111111111111000

Offset

1,2

Comments

a(18) is the first term that is neither a repunit nor the product of a repunit and a power of 10.

Links

David Radcliffe, Table of n, a(n) for n = 1..28

Example

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.

Maple

A004290:= proc(n)
local L, x, m, r, k, j;
for x from 2 to n-1 do L[0, x]:= 0 od:
L[0, 0]:= 1: L[0, 1]:= 1;
for m from 1 do
   if L[m-1, (-10^m) mod n] = 1 then break fi;
   L[m, 0]:= 1;
   for k from 1 to n-1 do
     L[m, k]:= max(L[m-1, k], L[m-1, k-10^m mod n])
   od;
od;
r:= 10^m; k:= -10^m mod n;
for j from m-1 by -1 to 1 do
    if L[j-1, k] = 0 then
      r:= r + 10^j; k:= k - 10^j mod n;
    fi
od;
if k = 1 then r:= r + 1 fi;
r
end proc:
A004290(1):= 1:
count:= 0: m:= 0;
for n from 1 to 20000 do
  v:= A004290(n);
  if v > m then
    count:= count+1;
    A[count]:= v;
    m:= v;
  fi
od:
seq(A[i], i=1..count); # Robert Israel, Feb 09 2016

Crossrefs

Cf. A004290, A268610. Subsequence of A007088.

Sequence in context: A286827 A286859 A290680 * A289937 A290062 A289929

Adjacent sequences: A268606 A268607 A268608 * A268610 A268611 A268612

Keyword

nonn,base

Author

David Radcliffe, Feb 08 2016

Extensions

a(1)=0 prepended to terms, b-file and Maple by Georg Fischer, Jun 24 2020

Initial 0 removed for consistency with change in A004290 by Sean A. Irvine, Feb 19 2024

Status

approved