Search: id:A097443
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%I A097443
%S A097443 13,31,43,67,71,83,89,107,151,157,163,191,197,199,227,283,293,307,311,
%T A097443 347,359,373,401,409,431,439,443,467,479,523,557,563,569,587,599,601,
%U A097443 631,653,677,683,719,761,787,827,839,877,881,883,911,919,929,947,991
%N A097443 Half-period primes, i.e. primes p for which reciprocal has period (p-1)/
               2.
%H A097443 T. D. Noe, <a href="b097443.txt">Table of n, a(n) for n=1..1000</a>
%H A097443 Makoto Kamada, <a href="http://homepage2.nifty.com/m_kamada/math/11111.htm">
               Factorizations of 11...11 (Repunit)</a>.
%H A097443 <a href="Sindx_1.html#1overn">Index entries for sequences related to 
               decimal expansion of 1/n</a>
%e A097443 13 is a half-period prime because 1/13 = 0.076923076923076923076923... 
               i.e. has period 6, or (13-1)/2.
%t A097443 f[n_Integer] := Block[{ds = Divisors[n - 1]}, (n - 1)/Take[ ds, Position[ 
               PowerMod[ 10, ds, n], 1] [[1, 1]]] [[ -1]]]; Select[ Prime[ Range[4, 
               200]], f[ # ] == 2 &] (from Robert G. Wilson v Sep 14 2004)
%Y A097443 Cf. A002371, A001913. Almost the same as A001914.
%Y A097443 Cf. A001913, A055628, A056157, A056210-A056217, A098680
%Y A097443 Sequence in context: A023274 A129864 A080387 this_sequence A100589 A111489 
               A106294
%Y A097443 Adjacent sequences: A097440 A097441 A097442 this_sequence A097444 A097445 
               A097446
%K A097443 nonn
%O A097443 1,1
%A A097443 Julien Peter Benney (jpbenney(AT)ftml.net), Aug 23 2004

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