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

2,1

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

Links

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

Example

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.

Prog

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

Crossrefs

A113516 gives the k values.

Cf. A076846, A084741, A084745, A346154.

Sequence in context: A084741 A135623 A172291 * A089305 A112618 A058027

Adjacent sequences: A343586 A343587 A343588 * A343590 A343591 A343592

Keyword

nonn

Author

Blake Branstool, Apr 20 2021

Extensions

Name revised by Peter Munn, Nov 16 2021

Status

approved