

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



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

1,2


COMMENTS

This sequence is infinite because 1/(10^n1) has a period of n for all n, so the period can be arbitrarily large.
Are 1, 3, 289 and 361 the only members that are not in A001913?  Robert Israel, Feb 10 2019


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


FORMULA

RECORDS transform of A051626.


EXAMPLE

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


MAPLE

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:
seq(A[i], i=1..count); # Robert Israel, Feb 10 2019


CROSSREFS

Cf. A051626.
Contains A001913.
Sequence in context: A227211 A271725 A058887 * A087749 A140863 A076194
Adjacent sequences: A306352 A306353 A306354 * A306356 A306357 A306358


KEYWORD

nonn,base


AUTHOR

Matthew Schulz, Feb 09 2019


STATUS

approved



