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A126017
Smallest prime of the form k^n + k^(n-1) - 1.
1
2, 5, 11, 23, 47, 971, 191, 383, 22136835839, 1310719, 2259801991, 6143, 353563778431304822783, 91424858111, 5425784582791, 57395627, 21474836479, 1099999999999999999, 786431, 13508517176729920889, 1818426107493966837974532393806148403199, 153558654482644991
OFFSET
1,1
COMMENTS
Primes arising in A125973.
EXAMPLE
Consider n = 10. k^n + k^(n-1) - 1 evaluates to 1, 1535, 78731, 1310719 for k = 1, ..., 4. Only the last of these numbers, 4^10+4^9-1 = 1310719, is prime, hence a(10) = 1310719.
MATHEMATICA
Table[k=0; Until[PrimeQ[p=k^n+k^(n-1)-1], k++]; p, {n, 22}] (* James C. McMahon, Dec 23 2024 *)
PROG
(PARI) {for(n=1, 20, k=1; while(!isprime(a=k^n+k^(n-1)-1), k++); print1(a, ", "))} \\ Klaus Brockhaus, Dec 17 2006
KEYWORD
nonn
AUTHOR
Artur Jasinski, Dec 14 2006
EXTENSIONS
Edited and extended by Klaus Brockhaus, Dec 17 2006
a(21)-a(22) from James C. McMahon, Dec 23 2024
STATUS
approved