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A362710
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Numbers m such that the decimal expansion of 1/m contains no digit 0, ignoring leading and trailing 0's.
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1
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 22, 24, 25, 26, 28, 30, 32, 35, 36, 40, 44, 45, 50, 54, 55, 56, 60, 64, 65, 66, 70, 72, 74, 75, 80, 82, 88, 90, 100, 104, 108, 112, 120, 125, 128, 132, 140, 144, 148, 150, 160, 175, 176, 180, 200, 216, 220, 224, 225, 240, 250, 252, 260, 264
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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If k is a term, then so is 10*k.
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LINKS
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EXAMPLE
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a(12) = 14 is a term because 1/14 = 0.0714285714... contains no digit 0 except for leading 0's.
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MAPLE
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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);
not(member(0, removeInitial0(NonRepeatingPart(q))) or member(0, RepeatingPart(q)))
end proc:
select(filter, [$1..300]);
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MATHEMATICA
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Select[Range[500], FreeQ[First[RealDigits[1/#]], 0] &] (* Paolo Xausa, Apr 22 2024 *)
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PROG
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(Python)
from itertools import count, islice
from sympy import multiplicity, n_order
def A362710_gen(startvalue=1): # generator of terms >= startvalue
for a in count(max(startvalue, 1)):
m2, m5 = (~a&a-1).bit_length(), multiplicity(5, a)
k, m = 10**max(m2, m5), 10**(t:=n_order(10, a//(1<<m2)//5**m5))-1
if not('0' in str(c:=k//a).lstrip('0') or ((w:=str(m*k//a-c*m).zfill(t)) != '0' and '0' in w)):
yield a
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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