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A306355
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Numbers k such that the period of 1/k, or 0 if 1/k terminates, is strictly greater than the period of the decimal expansion of 1/m for all m < k.
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1
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1, 3, 7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, 149, 167, 179, 181, 193, 223, 229, 233, 257, 263, 269, 289, 313, 337, 361, 367, 379, 383, 389, 419, 433, 461, 487, 491, 499, 503, 509, 541, 571, 577, 593, 619, 647, 659, 701, 709, 727, 743, 811, 821, 823
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OFFSET
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1,2
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COMMENTS
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This sequence is infinite because 1/(10^k-1) has a period of k for all k, so the period can be arbitrarily large.
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LINKS
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FORMULA
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EXAMPLE
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7 is a term because 1/7 has a period of 6, which is greater than the periods of 1/m for m < 7.
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MAPLE
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count:= 1: A[1]:= 1: m:= 0:
for k from 0 to 100 do
for d in [3, 7, 9, 11] do
x:= 10*k+d;
p:= numtheory:-order(10, x);
if p > m then
m := p;
count:= count+1;
A[count]:= x
fi
od od:
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MATHEMATICA
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ResourceFunction["ProgressiveMaxPositions"]@
Map[n |->
First[RealDigits[n]] /. {{___, list_?ListQ} :> Length[list],
list_?ListQ -> 0}][
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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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