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 A084738 Smallest prime of the form (n^k-1)/(n-1), or 0 if no such prime exists. 8
 3, 13, 5, 31, 7, 2801, 73, 0, 11, 50544702849929377, 13, 30941, 211, 241, 17, 307, 19, 109912203092239643840221, 421, 463, 23, 292561, 601, 0, 321272407, 757, 29, 732541, 31, 917087137, 0, 1123, 2458736461986831391 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS As mentioned by Dubner, when n is a power (greater than 1) of a prime, then (n^k-1)/(n-1) will usually be composite for all k, which is the case for n = 9, 25, 32 and 49. - T. D. Noe, Jan 23 2004 Here, a(n) is the smallest prime of the form (n^k-1)/(n-1) with k >= 2 while in A285642 it is the smallest prime with k > 2. Differences occur when (n^2-1)/(n-1) = n+1 is prime, and therefore, when n = prime(m) - 1 is in A006093 (see formula). - Bernard Schott, Mar 16 2023 LINKS Table of n, a(n) for n=2..34. H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930. FORMULA a(A006093(n)) = prime(n) for n >=2. - Bernard Schott, Mar 16 2023 EXAMPLE a(8) = 73 = (8^3-1)/(8-1). MATHEMATICA Table[SelectFirst[(n^# - 1)/(n - 1) & /@ Range[10^3], PrimeQ] /. k_ /; MissingQ@ k -> 0, {n, 2, 34}] (* Michael De Vlieger, Apr 24 2017, Version 10.2 *) CROSSREFS Cf. A076481. Cf. A084740 (least k such that (n^k-1)/(n-1) is prime). Cf. A006093, A285642. Sequence in context: A187023 A331806 A331807 * A352256 A073580 A340349 Adjacent sequences: A084735 A084736 A084737 * A084739 A084740 A084741 KEYWORD nonn AUTHOR Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 15 2003 EXTENSIONS More terms from T. D. Noe, Jan 23 2004 STATUS approved

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Last modified August 6 00:03 EDT 2024. Contains 374957 sequences. (Running on oeis4.)