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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
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).
Sequence in context: A187023 A331806 A331807 * A352256 A073580 A340349
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 March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)