

A152583


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


1




OFFSET

1,1


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^n1)+1) and 2^(2^n1)+1 is divisible by 3. This is evident from the identity, a^m+b^m = (a+b)(a^(m1)  a(m2)b + ... + b^(m1)) for odd m and 2^n1 is odd.


LINKS

Table of n, a(n) for n=1..7.


PROG

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


CROSSREFS

Sequence in context: A115204 A016277 A202131 * A304353 A305916 A134550
Adjacent sequences: A152580 A152581 A152582 * A152584 A152585 A152586


KEYWORD

nonn


AUTHOR

Cino Hilliard, Dec 08 2008


STATUS

approved



