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 A360761 Primes p that divide both 3^k-2 and 5^k-1 for some k. 0
 31, 601, 2593, 20478961, 204700049, 668731841 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If prime p divides 3^k-2 and 5^k-1, then p divides 3^j-2 and 5^j-1 for all j such that j == k (mod p-1). Primes p such that the equation 3^(x*A070677(p)) == 2 (mod p) has a solution. Values of k: 24, 108, 64, 376020, 67141466, 487515840, ... - Chai Wah Wu, Feb 24 2023 LINKS Table of n, a(n) for n=1..6. EXAMPLE a(3) = 2593 is a term because 2593 is prime, 3^64 == 2 (mod 2593) and 5^64 == 1 (mod 2593). MAPLE R:= NULL: count:= 0: p:= 5: with(numtheory): while count < 4 do p:= nextprime(p); if mlog(2, 3 &^ order(5, p) mod p, p) <> FAIL then R:= R, p; count:= count+1 fi od: R; PROG (Python) from itertools import islice from sympy import discrete_log, nextprime, n_order def A360761_gen(): # generator of terms p = 5 while True: try: discrete_log(p:=nextprime(p), 2, pow(3, n_order(5, p), p)) except: continue yield p A360761_list = list(islice(A360761_gen(), 4)) # Chai Wah Wu, Feb 23 2023 CROSSREFS Cf. A070677. Sequence in context: A240420 A022755 A003533 * A005462 A028201 A028184 Adjacent sequences: A360758 A360759 A360760 * A360762 A360763 A360764 KEYWORD nonn,more AUTHOR Robert Israel, Feb 19 2023 EXTENSIONS a(5)-a(6) from Chai Wah Wu, Feb 23 2023 STATUS approved

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Last modified September 27 17:53 EDT 2023. Contains 365714 sequences. (Running on oeis4.)