Search: id:A004022
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%I A004022 M4816
%S A004022 11,1111111111111111111,11111111111111111111111
%N A004022 Primes of form (10^n - 1)/9 (next terms are for n = 317, 1031, etc.).
%C A004022 Also called repunit primes.
%C A004022 The prime repunits, primes with digital product = 1.
%C A004022 The next term is too large to include: see A004023, A046413.
%C A004022 Contribution from Cino Hilliard (hillcino368(AT)hotmail.com), Dec 23 
               2008: (Start)
%C A004022 The number of 1's in these repunits must also be prime. Since the number 
               of
%C A004022 1's in (10^n-1)/9 is n, if n = pk then (10^pk-1)=(10^p)^k-1 => (10^p-1)/
               9 =
%C A004022 q and q divides (10^n-1). This follows from the identity,
%C A004022 a^n-b^n=(a-b)(a^(n-1)+a^(n-2)b+...+b^n-1). (End)
%D A004022 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A004022 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 
               1976, page 11.
%D A004022 J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, 
               Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and 
               later supplements.
%D A004022 Graham, Knuth and Patashnik, Concrete mathematics, Addison-Wesley, 1994; 
               see p 146 problem 22. [From Cino Hilliard (hillcino368(AT)hotmail.com), 
               Dec 23 2008]
%D A004022 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 
               60.
%H A004022 T. D. Noe, <a href="b004022.txt">Table of n, a(n) for n=1..5</a>
%H A004022 J. Brillhart et al., <a href="http://www.ams.org/online_bks/conm22/">
               Factorizations of b^n +- 1</a>, Contemporary Mathematics, Vol. 22, 
               Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
%H A004022 Andy Steward, <a href="http://www.users.globalnet.co.uk/~aads/primes.html">
               Prime Generalized Repunits</a>
%H A004022 S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/
               cun/index.html">The Cunningham Project</a>
%t A004022 lst={};Do[If[PrimeQ[p=(10^n-1)/9], AppendTo[lst, p]], {n, 10^2}];lst 
               [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 22 2008]
%o A004022 Contribution from Cino Hilliard (hillcino368(AT)hotmail.com), Dec 23 
               2008: (Start)
%o A004022 (PARI) forprime(x=2,20000,if(ispseudoprime((10^x-1)/9),print1((10^x-1)/
               9",")))
%o A004022 (End)
%Y A004022 See A046413 for the number of 1's. Cf. A004023.
%Y A004022 Sequence in context: A072218 A046844 A066953 this_sequence A083344 A063863 
               A101364
%Y A004022 Adjacent sequences: A004019 A004020 A004021 this_sequence A004023 A004024 
               A004025
%K A004022 nonn,nice,bref
%O A004022 1,1
%A A004022 N. J. A. Sloane (njas(AT)research.att.com).

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