A343589 Smallest prime of the form n^k-(n-1) or 0 if no such prime exists.

3, 7, 13, 3121, 31, 43, 549755813881, 73, 991, 1321, 248821, 157, 2731, 211, 241, 34271896307617, 307, 6841, 13107199999999999999981, 421, 463, 141050039560662968926081, 331753, 601, 17551, 7625597484961, 757, 1816075630094014572464024421543167816955354437761

Offset: 2

Author

Blake Branstool, Apr 20 2021

Keywords

• nonn

Comments

All values up to n=70 have been found and proved to be primes. n=71 has k=3019 and gives a probable prime.

See A113516, which gives the k values and is the main entry for these primes, for more extensively researched information. - Peter Munn, Nov 20 2021

Examples

			For n=2 and k=2, 2^2-(2-1)=3 thus a(2)=3. k is 2 as well for n=3,4.
For n=5 the first k to result in a prime is 5, 5^5-(5-1)=3121 thus a(5)=3121.
		

Links

• Blake Branstool, Table of n, a(n) for n = 2..70

Crossrefs

A113516 gives the k values.

Cf. A076846, A084741, A084745, A346154.

Programs

PARI

a(n) = my(k=1, p); while (!isprime(p=n^k-(n-1)), k++); p; \\ Michel Marcus, Nov 17 2021

Extensions

Name revised by Peter Munn, Nov 16 2021