Search: id:A028416
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%I A028416
%S A028416 7,11,13,17,19,23,29,47,59,61,73,89,97,101,103,109,113,127,131,137,139,
%T A028416 149,157,167,179,181,193,197,211,223,229,233,241,251,257,263,269,281,
%U A028416 293,313,331,337,349,353,367,373,379,383,389,401,409,419,421,433
%N A028416 Primes p such that the decimal expansion of 1/p has a periodic part of 
               even length.
%C A028416 Primes whose reciprocals have even period length.
%C A028416 A002371(A049084(a(n))) mod 2 == 0.
%C A028416 Not the same as A040121: a(33)=241 is not in A040121.
%C A028416 Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 05 2008: (Start)
%C A028416 Let (d(i): 1<=i<=2*K) be the period of decimal expansion of 1/a(n), K=A002371(A049084(a(n)))/
               2,
%C A028416 then d(i) + d(i+K) = 9 for i with 1<=i<=K, or, equivalently:
%C A028416 u + v = 10^K - 1 with u=SUM(d(i)*10^(K-i):1<=i<=K) and v=SUM(d(i+K)*10^(K-i):1<=i<=K). 
               (End)
%D A028416 H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, 
               reprinted 1968), ch. 19, 'Die periodischen Dezimalbrueche'. [From 
               Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 05 2008]
%H A028416 <a href="Sindx_1.html#1overn">Index entries for sequences related to 
               decimal expansion of 1/n.</a>
%e A028416 Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 05 2008: (Start)
%e A028416 (0,5,8,8,2,3,5,2,9,4,1,1,7,6,4,7) is the period of 1/17 (see A007450),
%e A028416 K = A002371(A049084(17))/2 = A002371(7)/2 = 16/2 = 8,
%e A028416 u = 5882352, v = 94117647: u + v = 99999999 = 10^8 - 1. (End)
%Y A028416 Cf. A087000.
%Y A028416 Sequence in context: A135776 A067831 A086998 this_sequence A040121 A156114 
               A091554
%Y A028416 Adjacent sequences: A028413 A028414 A028415 this_sequence A028417 A028418 
               A028419
%K A028416 nonn,base
%O A028416 1,1
%A A028416 Mario Velucchi (mathchess(AT)velucchi.it)
%E A028416 More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jul 29 2003

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