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A167791 Numbers with primitive root 2. 30
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

MATHEMATICA

pr=2; Select[Range[2, 2000], MultiplicativeOrder[pr, # ] == EulerPhi[ # ] &]

PROG

(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

CROSSREFS

Cf. A001122 (primes with primitive root 2).

Sequence in context: A007950 A034936 A204657 * A139099 A152259 A219611

Adjacent sequences: A167788 A167789 A167790 * A167792 A167793 A167794

KEYWORD

nonn

AUTHOR

T. D. Noe, Nov 12 2009

STATUS

approved

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Last modified December 9 19:36 EST 2022. Contains 358703 sequences. (Running on oeis4.)