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 A028416 Primes p such that the decimal expansion of 1/p has a periodic part of even length. 13
 7, 11, 13, 17, 19, 23, 29, 47, 59, 61, 73, 89, 97, 101, 103, 109, 113, 127, 131, 137, 139, 149, 157, 167, 179, 181, 193, 197, 211, 223, 229, 233, 241, 251, 257, 263, 269, 281, 293, 313, 331, 337, 349, 353, 367, 373, 379, 383, 389, 401, 409, 419, 421, 433 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Primes whose reciprocals have even period length. Primes p such that the order of 10 mod p is even. - Joerg Arndt, Mar 04 2014 A002371(A049084(a(n))) mod 2 == 0. Not the same as A040121: a(33)=241 is not in A040121. Let (d(i): 1<=i<=2*K) be the period of the decimal expansion of 1/a(n), K=A002371(A049084(a(n)))/2, then d(i) + d(i+K) = 9 for i with 1<=i<=K, or, equivalently: u + v = 10^K - 1 with u = Sum_{i=1..K} d(i)*10^(K-i) and v = Sum_{i=1..K} d(i+K)*10^(K-i). - Reinhard Zumkeller, Oct 05 2008 REFERENCES H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, reprinted 1968), ch. 19, "Die periodischen Dezimalbrueche". [Reinhard Zumkeller, Oct 05 2008] LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 Index entries for sequences related to decimal expansion of 1/n. EXAMPLE From Reinhard Zumkeller, Oct 05 2008: (Start) (0,5,8,8,2,3,5,2,9,4,1,1,7,6,4,7) is the period of 1/17 (see A007450), K = A002371(A049084(17))/2 = A002371(7)/2 = 16/2 = 8, u = 5882352, v = 94117647: u + v = 99999999 = 10^8 - 1. (End) MAPLE A028416 := proc(n) local st: st := ithprime(n): if (modp(numtheory[order](10, st), 2) = 0) then RETURN(st) fi: end: seq(A028416(n), n=1..100); # Jani Melik, Feb 24 2011 MATHEMATICA Select[Prime[Range[4, 100]], EvenQ[Length[RealDigits[1/#][[1, 1]]]]&] (* Harvey P. Dale, Jul 07 2011 *) PROG (PARI) forprime(p=7, 1e3, if(znorder(Mod(10, p))%2==0, print1(p", "))) \\ Charles R Greathouse IV, Feb 24 2011 CROSSREFS Cf. A087000, A186635. Sequence in context: A135776 A067831 A086998 * A040121 A156114 A304690 Adjacent sequences: A028413 A028414 A028415 * A028417 A028418 A028419 KEYWORD nonn,base AUTHOR Mario Velucchi (mathchess(AT)velucchi.it) EXTENSIONS More terms from Reinhard Zumkeller, Jul 29 2003 STATUS approved

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Last modified February 27 10:59 EST 2024. Contains 370378 sequences. (Running on oeis4.)