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

2,1

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