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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is infinite because 1/(10^n-1) 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

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Last modified December 8 09:32 EST 2019. Contains 329862 sequences. (Running on oeis4.)