* $a^n \pm 1$ for $a = 2, 3, 5, 6, 7, 10, 11, 12$ and large exponents n [[http://homes.cerias.purdue.edu/~ssw/cun/index.html]]
 * $a^n \pm 1$ for $a ≤ 13$ and $a$ not a perfect number [[http://wwwmaths.anu.edu.au/~brent/factors.html]]
 * $2^n \pm 1$ for $1200 < n < 10000$ [[http://www.euronet.nl/users/bota/medium-p.htm]]
 * $10^n \pm 1$ for $n ≤ 100$ [[http://www.swox.com/gmp/repunit.html]]
 * $p^p \pm 1$ where $p$ is a prime number and $p < 180$. [[http://homes.cerias.purdue.edu/~ssw/bell]]
 * $2^{2^n} + 1$ (Fermat numbers) [[http://www.prothsearch.net/fermat.html]]
 * $2^{3^n} \pm 1$ [[http://www.alpertron.com.ar/MODFERM.HTM]] 
 * Fibonacci numbers ($F_n$) and Lucas numbers ($L_n$) for $n < 10000$ [[http://home.att.net/~blair.kelly/mathematics/fibonacci/]]
 * $n*2^n \pm 1$ (Cullen and Woodall numbers) [[http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.htm]]
 * Euclid numbers [[http://en.wikipedia.org/wiki/Sylvester's_sequence#Divisibility_and_factorizations]]