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

Author

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

Keywords

• nonn

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

Examples

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

Links

• 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.

Crossrefs

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

Extensions

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