A084741 Smallest prime of the form (n^k+1)/(n+1), or 0 if no such prime exists.

3, 7, 13, 521, 31, 43, 0, 73, 9091, 13421, 19141, 157, 7027567, 211, 241, 22796593, 307, 274019342889240109297, 152381, 421, 463, 39700406579747, 183458857, 601, 135938684703251, 0, 757, 574995877

Offset

2,1

Comments

When n is a power (greater than 2) of a prime, then (n^k+1)/(n+1) will usually be composite for all k, which is the case for n = 8, 27, 32, 64, 125. The next term, a(30), is a 204-digit number. - T. D. Noe, Jan 22 2004

Links

Table of n, a(n) for n=2..29.

H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.

R. G. Wilson, v, Letter to N. J. A. Sloane, circa 1991.

Example

a(7)= 43 = (7^3 +1 )/(7+1) = 1 - 7 + 7^2 is a prime.

Crossrefs

Cf. A084742 (least k such that (n^k+1)/(n+1) is prime).

Sequence in context: A322301 A154821 A353008 * A135623 A172291 A343589

Adjacent sequences: A084738 A084739 A084740 * A084742 A084743 A084744

Keyword

nonn

Author

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

Extensions

More terms from T. D. Noe, Jan 22 2004

Status

approved