A152583 Numbers of the form 11^(2^n) + 2.

13, 123, 14643, 214358883, 45949729863572163, 2111377674535255285545615254209923, 4457915684525902395869512133369841539490161434991526715513934826243

Offset: 1

Author

Cino Hilliard, Dec 08 2008

Keywords

• nonn

Comments

Except for the first term, these numbers are divisible by 3. This follows from the binomial expansion of (9+2)^(2^n)+2 = 9h + 2^(2^n)+2. Now 2^(2^n)+2 can be written as 2*(2^(2^n-1)+1) and 2^(2^n-1)+1 is divisible by 3. This is evident from the identity, a^m+b^m = (a+b)(a^(m-1) - a(m-2)b + ... + b^(m-1)) for odd m and 2^n-1 is odd.

Programs

PARI

g(a,n) = if(a%2,b=2,b=1);for(x=0,n,y=a^(2^x)+b;print1(y","))