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A167791
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Numbers with primitive root 2.
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30
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3, 5, 9, 11, 13, 19, 25, 27, 29, 37, 53, 59, 61, 67, 81, 83, 101, 107, 121, 125, 131, 139, 149, 163, 169, 173, 179, 181, 197, 211, 227, 243, 269, 293, 317, 347, 349, 361, 373, 379, 389, 419, 421, 443, 461, 467, 491, 509, 523, 541, 547, 557, 563, 587, 613, 619
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OFFSET
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1,1
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COMMENTS
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Numbers n such that the binary expansion of 1/n has period phi(n). For example 1/27 has a period of 18 bits.
All entries are odd. An odd composite number n can have a primitive root if and only if it is a prime power (see A033948). - V. Raman, Oct 04 2012
It is unknown whether there is a prime p such that p is in this sequence while p^2 is not. - Jianing Song, Jan 27 2019
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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MATHEMATICA
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pr=2; Select[Range[2, 2000], MultiplicativeOrder[pr, # ] == EulerPhi[ # ] &]
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PROG
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(PARI) for(n=3, 200, if(n%2==1&&znorder(Mod(2, n))==eulerphi(n), printf(n", "))) \\ V. Raman, Oct 04 2012
(PARI) is(n)=n%2 && isprimepower(n) && znorder(Mod(2, n))==eulerphi(n-1) \\ Charles R Greathouse IV, Jul 05 2013
(Magma) [n: n in [3..619] | IsPrimitive(2, n)]; // Arkadiusz Wesolowski, Dec 22 2020
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CROSSREFS
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Cf. A001122 (primes with primitive root 2).
Sequence in context: A007950 A034936 A204657 * A139099 A152259 A219611
Adjacent sequences: A167788 A167789 A167790 * A167792 A167793 A167794
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe, Nov 12 2009
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STATUS
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approved
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