1,1

Also called full repetend primes or maximal period primes.

Also called golden primes or long primes.

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.

Albert H. Beiler, Recreations in the Theory of Numbers, 2nd ed. New York: Dover, 1966, pages 65, 309.

John H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, p. 161.

Carl Friedrich Gauss, "Disquitiones Arithmeticae"

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 115.

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. 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.]

C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Oxford University Press, 1966, pp. 56-58.

T. D. Noe, Table of n, a(n) for n=1..1000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to decimal expansion of 1/n

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:

(2*1-1)(3*2-1)(5*4-1)(7*6-1)(11*10-1)(13*12-1)...

-------------------------------------------------

(2*1)(3*2)(5*4)(7*6)(11*10)(13*12)...

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)

Apart from initial term, identical to A001913. Cf. A006559, A067556.

Adjacent sequences: A006880 A006881 A006882 this_sequence A006884 A006885 A006886

Sequence in context: A073998 A129444 A079815 this_sequence A023269 A023300 A045378

nonn,nice,easy

mrob(AT)mrob.com (Robert P Munafo)

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.