login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A152583
Numbers of the form 11^(2^n) + 2.
1
13, 123, 14643, 214358883, 45949729863572163, 2111377674535255285545615254209923, 4457915684525902395869512133369841539490161434991526715513934826243
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^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.
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
KEYWORD
nonn
AUTHOR
Cino Hilliard, Dec 08 2008
STATUS
approved