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%I #12 Apr 18 2017 07:47:45
%S 3,27,33,333,369,909,2151,2439,2997,3333,27027,33333,37683,41841,
%T 76923,90909,142857,194841,243603,333333
%N Numbers n (relatively prime to 10) such that the decimal form of the period of 1/n is prime.
%C This sequence is infinite because the numbers 3, 33, 333, ... generate the decimal form 3. The correspondant primes of this sequence such that :
%C {3, 37, 3, 3, 271, 11, 4649, 41, 333667, 3} are included in the sequence A178505.
%C The Maple program below is very slow for the numbers > 3333.
%D H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, reprinted 1968), ch. 19, 'Die periodischen Dezimalbrueche'.
%H <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n.</a>
%e 27 is in the sequence because 1/27 = 0.037 037 ... and 37 is prime.
%e 2997 is in the sequence because 1/2997 = 0.000333667 000333667 ... and 333667 is prime.
%p with(numtheory): Digits:=4000:nn:=4000:for n from 3 by 2 to nn do:z:=evalf(1/n): indic:=0:for p from 1 to nn do:if irem(10^p, n) = 1 and gcd(n, 5) = 1 and indic=0 then pp:=p:indic:=1:z1:=floor(z*10^pp): else fi:od:if indic=1 and type(z1,prime)=true then print(n):else fi:od:
%Y Cf. A178505, A045572, A002329.
%K nonn,base
%O 1,1
%A _Michel Lagneau_, Jun 24 2010
%E Extended and name corrected by _T. D. Noe_, Nov 18 2010
%E a(17)-a(20) from _Ray Chandler_, Apr 17 2017
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