The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A081318

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A081318

Integers n such that the reciprocal of the largest prime factor of 10^n-1 is not a repeating decimal fraction with a period of n.
(history; published version)

#20 by Max Alekseyev at Tue Apr 26 18:45:06 EDT 2022

STATUS

editing

approved

#19 by Max Alekseyev at Tue Apr 26 18:45:02 EDT 2022

DATA

6, 18, 22, 30, 32, 38, 42, 46, 54, 66, 74, 78, 82, 90, 94, 96, 110, 118, 132, 138, 146, 154, 162, 174, 186, 194, 198, 206, 210, 218, 228, 231, 240, 242, 254, 258, 260, 264, 266, 268, 274, 282, 284, 286, 298, 300, 306, 310, 318, 322, 334, 338, 344, 348

EXTENSIONS

a(42)-a(5054) from Max Alekseyev, Aug 17 2013, Apr 26 2022

STATUS

approved

editing

#18 by Charles R Greathouse IV at Thu Jan 17 13:44:06 EST 2019

LINKS

Makoto Kamada, <a href="httphttps://stdkmd.comnet/nrr/repunit/"> Factorizations of 11...11 (repunit)</a>.

Discussion

Thu Jan 17

13:44

OEIS Server: https://oeis.org/edit/global/2791

#17 by Joerg Arndt at Mon Apr 30 11:06:37 EDT 2018

STATUS

reviewed

approved

#16 by Michel Marcus at Mon Apr 30 01:02:11 EDT 2018

STATUS

proposed

reviewed

#15 by Jon E. Schoenfield at Mon Apr 30 00:37:46 EDT 2018

STATUS

editing

proposed

#14 by Jon E. Schoenfield at Mon Apr 30 00:37:43 EDT 2018

NAME

Integers n such that the reciprocal of the largest prime factor of 10^n-1 is not a repeating decimal fraction with a period of length n.

EXAMPLE

30 is in the sequence because the factorization of 10^30-1 is 3^3*7*11*13*31*37*41*211*241*271*2161*9091*2906161 and 2906161 occurs already in 10^15-1=3^3*31*37*41*271*2906161 producing a decimal fraction with a period of 15, (1/2906161=0.000000344096559000000344096559000000344...)

STATUS

approved

editing

#13 by Jon E. Schoenfield at Mon Feb 27 01:33:45 EST 2017

STATUS

editing

approved

#12 by Jon E. Schoenfield at Mon Feb 27 01:33:35 EST 2017

COMMENTS

For all but three of the terms through a(41)=274, the reciprocal of the largest prime factor of 10^a(n)-1 is a decimal fraction with a period of a(n)/2. Of the three exceptions, there are two (a(32)=231 and a(38)=264) where the period is a(n)/3, and one (a(19)=132) where the period is a(n)/4. [From _- _Jon E. Schoenfield_, Jun 27 2010]

STATUS

approved

editing

#11 by N. J. A. Sloane at Wed Apr 22 17:57:14 EDT 2015

LINKS

Makoto Kamada, <a href="http://homepage2.niftystdkmd.com/m_kamadanrr/mathrepunit/11111.htm"> Factorizations of 11...11 (repunit)</a>.

Discussion

Wed Apr 22

17:57

OEIS Server: https://oeis.org/edit/global/2427