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A343589
Smallest prime of the form n^k-(n-1) or 0 if no such prime exists.
2
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
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.
Sequence in context: A084741 A135623 A172291 * A089305 A112618 A058027
KEYWORD
nonn
AUTHOR
Blake Branstool, Apr 20 2021
EXTENSIONS
Name revised by Peter Munn, Nov 16 2021
STATUS
approved