OFFSET
1,1
COMMENTS
Leading 0's are not considered, otherwise every integer >= 11 would be a term (see examples).
Trailing 0's are also not considered, otherwise numbers of the form 2^i*5^j with i, j >= 0, apart 1 (A003592) would be terms.
If k is a term, 10*k is also a term; so, terms with no trailing zeros are all primitive.
Some subsequences:
{11, 111, 1111, ...} = A002275 \ {0, 1}
{33, 333, 3333, ...} = A002277 \ {0, 3}.
{77, 777, 7777, ...} = A002281 \ {0, 7}
{11, 101, 1001, 10001, ...} = A000533 \ {1}.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
A352153(a(n)) = 0.
EXAMPLE
m = 13 is a term since 1/13 = 0.0769230769230769230... has a periodic part = '07692307' or '76923070' with a 0.
m = 14 is not a term since 1/14 = 0.0714285714285714285... has a periodic part = '714285' which has no 0 (the only 0 is a leading 0).
MAPLE
removeInitial0:= proc(L) local i;
for i from 1 to nops(L) do if L[i] <> 0 then return L[i..-1] fi od;
[]
end proc:
filter:= proc(n) local q;
q:= NumberTheory:-RepeatingDecimal(1/n);
member(0, removeInitial0(NonRepeatingPart(q))) or member(0, RepeatingPart(q))
end proc:
select(filter, [$1..300]); # Robert Israel, Apr 26 2023
MATHEMATICA
f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 200, Min@ f@# == 0 &]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernard Schott and Robert G. Wilson v, Mar 14 2022
STATUS
approved