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%I #20 Apr 26 2022 18:45:06
%S 6,18,22,30,32,38,42,46,54,66,74,78,82,90,94,96,110,118,132,138,146,
%T 154,162,174,186,194,198,206,210,218,228,231,240,242,254,258,260,264,
%U 266,268,274,282,284,286,298,300,306,310,318,322,334,338,344,348
%N 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.
%C 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. - _Jon E. Schoenfield_, Jun 27 2010
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/repunit/"> Factorizations of 11...11 (repunit)</a>.
%F Integers n such that A061075(n) is not equal to A005422(n).
%e 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...)
%Y Cf. A081317.
%K more,nonn
%O 1,1
%A _Hugo Pfoertner_, Mar 18 2003
%E More terms from _Hans Havermann_, May 31 2003
%E Terms a(31)-a(37) from _Jon E. Schoenfield_, Jun 19 2010
%E Terms a(38)-a(41) added, link added, and earlier comment expanded by _Jon E. Schoenfield_, Jun 27 2010
%E a(42)-a(54) from _Max Alekseyev_, Aug 17 2013, Apr 26 2022
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