%I A006883 M1745 N1823
%S A006883 2,7,17,19,23,29,47,59,61,97,109,113,131,149,167,179,181,193,223,229,
%T A006883 233,257,263,269,313,337,367,379,383,389,419,433,461,487,491,499,503,
%U A006883 509,541,571,577,593,619,647,659,701,709,727,743,811,821,823,857,863
%N A006883 Long period primes: 1/p has period p-1.
%C A006883 Also called full repetend primes or maximal period primes.
%C A006883 Also called golden primes or long primes.
%D A006883 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 864.
%D A006883 Albert H. Beiler, Recreations in the Theory of Numbers, 2nd ed. New York: 
               Dover, 1966, pages 65, 309.
%D A006883 John H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, 
               p. 161.
%D A006883 Carl Friedrich Gauss, "Disquitiones Arithmeticae"
%D A006883 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 
               3rd ed., Oxford Univ. Press, 1954, p. 115.
%D A006883 M. Kraitchik, Recherches sur la Th\'{e}orie des Nombres. Gauthiers-Villars, 
               Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 61.
%D A006883 D. H. Lehmer, A note on primitive roots, Scripta Mathematica, vol. 26 
               (1963), p. 117. [Gives some interesting information about the frequency 
               of maximal period primes and discusses two freak cases.]
%D A006883 C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, 
               Oxford University Press, 1966, pp. 56-58.
%D A006883 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A006883 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006883 T. D. Noe, <a href="b006883.txt">Table of n, a(n) for n=1..1000</a>
%H A006883 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A006883 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FullReptendPrime.html">Link to a section of The World of Mathematics.</
               a>
%H A006883 <a href="Sindx_1.html#1overn">Index entries for sequences related to 
               decimal expansion of 1/n</a>
%F A006883 Comment from Gerard Schildberger (GerardS(AT)rrt.net), Jul 02 2005: Emil 
               Artin conjectured that the proportion of primes that belong to this 
               sequence can be expressed as:
%F A006883 (2*1-1)(3*2-1)(5*4-1)(7*6-1)(11*10-1)(13*12-1)...
%F A006883 -------------------------------------------------
%F A006883 (2*1)(3*2)(5*4)(7*6)(11*10)(13*12)...
%p A006883 isA006883 := proc(p) if p = 2 then true; elif isprime(p) then RETURN( 
               numtheory[order](10,p) = p-1) ; else false; fi; end: for i from 1 
               to 300 do p := ithprime(i) ; if isA006883(p) then printf("%d ",p) 
               ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 
               01 2009]
%t A006883 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, 
               150]], f[ # ] == 1 &] (from Robert G. Wilson v Sep 14 2004)
%Y A006883 Apart from initial term, identical to A001913. Cf. A006559, A067556.
%Y A006883 Sequence in context: A073998 A129444 A079815 this_sequence A023269 A023300 
               A045378
%Y A006883 Adjacent sequences: A006880 A006881 A006882 this_sequence A006884 A006885 
               A006886
%K A006883 nonn,nice,easy
%O A006883 1,1
%A A006883 mrob(AT)mrob.com (Robert P Munafo)
%E A006883 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 21 2000. 
               Additional comments from Jason Earls (zevi_35711(AT)yahoo.com), Apr 
               06 2001.