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A344202 Primes p such that gcd(ord_p(2), ord_p(3)) = 1. 0
683, 599479, 108390409, 149817457, 666591179, 2000634731, 4562284561, 14764460089, 24040333283, 2506025630791, 5988931115977 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Related to Diophantine equations of the form (2^x-1)*(3^y-1) = n*z^2.

LINKS

Table of n, a(n) for n=1..11.

Sofia Lacerda, C++ program (github).

Mathoverflow, Solve this Diophantine equation (2^x-1)(3^y-1)=2z^2

MATHEMATICA

Select[Range[10^6], PrimeQ[#] && CoprimeQ[MultiplicativeOrder[2, #], MultiplicativeOrder[3, #]] &] (* Amiram Eldar, May 11 2021 *)

PROG

(C++) see link

(PARI) isok(p) = isprime(p) && (gcd(znorder(Mod(2, p)), znorder(Mod(3, p))) == 1); \\ Michel Marcus, May 11 2021

(Python)

from sympy.ntheory import n_order

from sympy import gcd, nextprime

A344202_list, p = [], 5

while p < 10**9:

    if gcd(n_order(2, p), n_order(3, p)) == 1:

        A344202_list.append(p)

    p = nextprime(p) # Chai Wah Wu, May 12 2021

CROSSREFS

Cf. A014664, A062117.

Sequence in context: A269486 A239272 A076574 * A015386 A245393 A252856

Adjacent sequences:  A344199 A344200 A344201 * A344203 A344204 A344205

KEYWORD

nonn,more,hard

AUTHOR

Sofia Lacerda, May 11 2021

EXTENSIONS

a(3)-a(5) from Michel Marcus, May 11 2021

a(6)-a(8) from Amiram Eldar, May 11 2021

a(9) from Daniel Suteu, May 16 2021

a(10) from Sofia Lacerda, Jul 07 2021

a(11) from Sofia Lacerda, Aug 03 2021

STATUS

approved

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Last modified January 26 22:05 EST 2022. Contains 350601 sequences. (Running on oeis4.)