OFFSET
1,1
COMMENTS
For n > 1, smallest prime of the form ((p-1)^prime(n)+1)/p, where p is prime; the corresponding primes p are A237115(n) = 3, 3, 3, 3, 3, 3, 3, 3, 691, 3, 17, ... and the corresponding semiprimes (p-1)^prime(n)+1 are A237114(n) = 9, 33, 129, 2049, 8193, 131073, 524289, 8388609, ... .
It appears that a(n) == 1 (mod prime(n)), for all n <> 2. See 4th comment in A237114.
LINKS
FORMULA
EXAMPLE
Prime(1)=2 and the smallest semiprime of the form k^2+1 is 3^2+1 = 10 = 2*5, so a(1) = 5.
Prime(2)=3 and the smallest semiprime of the form k^3+1 is 2^3+1 = 9 = 3*3, so a(2) = 3.
MATHEMATICA
L = {5}; Do[p = Prime[k]; n = 1; q = Prime[n] - 1; cp = (q^p + 1)/(q + 1); While[! PrimeQ[cp], n = n + 1; q = Prime[n] - 1; cp = (q^p + 1)/(q + 1)]; L = Append[L, cp], {k, 2, 13}]; L
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Feb 05 2014
STATUS
approved