OFFSET
1,1
COMMENTS
There can never be an odd term! Proof. Any odd semiprime is of the form p*q, with 2 < p <= q. Therefore p^q +1 is even. Also p^q+1 is divisible by p+1 and p+1 is greater than 3 and it is even. Therefore p+1 has at least two divisors and we are still left with the factor (p^q+1)/(p+1). QED
LINKS
Dario Alejandro Alpern, Factorization using the Elliptic Curve Method
EXAMPLE
38=2*19 is a member because 19^2+1=362=2*181.
MATHEMATICA
PrimeFactors[n_Integer] := Flatten[ Table[ # [[1]], { # [[2]]}] & /@ FactorInteger[n]]; a = {}; Do[p = PrimeFactors[n]; If[ Length[p] == 2 && Length[ PrimeFactors[ p[[2]]^p[[1]] + 1]] == 2, AppendTo[a, n]], {n, 1000}]; a
CROSSREFS
KEYWORD
nonn
AUTHOR
Jason Earls, Jul 19 2003
EXTENSIONS
Edited and extended by Robert G. Wilson v, Jul 19 2003
STATUS
approved