A084738 Smallest prime of the form (n^k-1)/(n-1), or 0 if no such prime exists.

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

Offset: 2

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 15 2003

Keywords

• nonn

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

Examples

			a(8) = 73 = (8^3-1)/(8-1).
		

Links

• H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.

Crossrefs

Cf. A076481.

Cf. A084740 (least k such that (n^k-1)/(n-1) is prime).

Cf. A006093, A285642.

Programs

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 *)

Formula

a(A006093(n)) = prime(n) for n >=2. - Bernard Schott, Mar 16 2023

Extensions

More terms from T. D. Noe, Jan 23 2004