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A306355 Numbers n such that the period of 1/n, or 0 if 1/n terminates, is strictly greater than the periods of the decimal expansions of 1/m beforehand. 1

%I

%S 1,3,7,17,19,23,29,47,59,61,97,109,113,131,149,167,179,181,193,223,

%T 229,233,257,263,269,289,313,337,361,367,379,383,389,419,433,461,487,

%U 491,499,503,509,541,571,577,593,619,647,659,701,709,727,743,811,821,823

%N Numbers n such that the period of 1/n, or 0 if 1/n terminates, is strictly greater than the periods of the decimal expansions of 1/m beforehand.

%C This sequence is infinite because 1/(10^n-1) has a period of n for all n, so the period can be arbitrarily large.

%C Are 1, 3, 289 and 361 the only members that are not in A001913? - _Robert Israel_, Feb 10 2019

%H Robert Israel, <a href="/A306355/b306355.txt">Table of n, a(n) for n = 1..10000</a>

%F RECORDS transform of A051626.

%e 7 is a term because 1/7 has a period of 6, which is greater than the periods of 1/m for m<7.

%p count:= 1: A[1]:= 1: m:= 0:

%p for k from 0 to 100 do

%p for d in [3,7,9,11] do

%p x:= 10*k+d;

%p p:= numtheory:-order(10,x);

%p if p > m then

%p m := p;

%p count:= count+1;

%p A[count]:= x

%p fi

%p od od:

%p seq(A[i],i=1..count); # _Robert Israel_, Feb 10 2019

%Y Cf. A051626.

%Y Contains A001913.

%K nonn,base

%O 1,2

%A _Matthew Schulz_, Feb 09 2019

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Last modified January 21 13:55 EST 2020. Contains 331113 sequences. (Running on oeis4.)