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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 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.)