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A320384 Primes p such that 3/2 is a primitive root modulo p. 1
7, 11, 17, 31, 37, 41, 59, 83, 89, 103, 107, 109, 113, 127, 131, 137, 151, 157, 179, 223, 227, 229, 233, 251, 257, 271, 277, 347, 349, 353, 367, 397, 421, 443, 449, 467, 491, 521, 541, 563, 569, 587, 593, 607, 613, 631, 641, 659, 661, 683, 733, 757, 761, 809, 827, 853, 857, 877, 929, 953, 967, 971, 977, 991 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes p such that the smallest positive k such that p divides 3^k - 2^k is p - 1.

All terms are congruent to 7, 11, 13, 17 modulo 24. For other primes p, 3/2 is a quadratic residue modulo p.

By Artin's conjecture, this sequence contains 37.395% of all primes, or 74.79% of all primes congruent to 7, 11, 13, 17 modulo 24.

LINKS

Table of n, a(n) for n=1..64.

C. Hooley, On Artin's conjecture, J. reine angewandte Math., 225 (1967) 209-220.

Wikipedia, Artin's conjecture on primitive roots

Wikipedia, Primitive root modulo n

Index entries for sequences related to Artin's conjecture

Index entries for primes by primitive root

EXAMPLE

3/2 == 5 (mod 7), 5 is a primitive root modulo 7, so 7 is a term. Indeed, 7 does not divide 3^2 - 2^2 or 3^3 - 2^3, but it divides 3^6 - 2^6.

3/2 == 7 (mod 11), 7 is a primitive root modulo 11, so 11 is a term. Indeed, 11 does not divide 3^2 - 2^2 or 3^5 - 2^5, but it divides 3^10 - 2^10.

3/2 == 13 (mod 23), 13^11 == 1 (mod 23), so 23 is not a term. Indeed, 23 divides 3^11 - 2^11.

PROG

(PARI) forprime(p=5, 10^3, if(p-1==znorder(Mod(3/2, p)), print1(p, ", "))); \\ Joerg Arndt, Oct 13 2018

CROSSREFS

Cf. A019336, A320383.

Sequence in context: A078725 A247478 A174360 * A019418 A068674 A156112

Adjacent sequences:  A320381 A320382 A320383 * A320385 A320386 A320387

KEYWORD

nonn

AUTHOR

Jianing Song, Oct 12 2018

STATUS

approved

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Last modified May 14 07:13 EDT 2021. Contains 343879 sequences. (Running on oeis4.)