1,1

These numbers are all composite. We re-write 8^(2^n) + 1 = (2^(2^n))^3 + 1.

Then by the identity a^n+b^n = (a+b)(a^(n-1) - a^(n-2)b + ... + b^(n-1)) for

odd n, 2^(2^n) + 1 divides 8^(2^n) + 1.

For n = 3, 8^(2^3)+1 = 16777217. Similarly, (2^8)^3 + 1 = 16777217. Then

then 2^8+1 = 257 and 16777217/257 = 65281.

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

Sequence in context: A103459 A100311 A120286 this_sequence A122733 A118465 A051375

Adjacent sequences: A152578 A152579 A152580 this_sequence A152582 A152583 A152584

nonn

Cino Hilliard (hillcino368(AT)hotmail.com), Dec 08 2008