A130730 Fermat numbers of order 7 or F(n,7) = 2^(2^n)+7.

9, 11, 23, 263, 65543, 4294967303, 18446744073709551623, 340282366920938463463374607431768211463, 115792089237316195423570985008687907853269984665640564039457584007913129639943

Offset: 0

Author

Cino Hilliard, Jul 05 2007

Keywords

• nonn

Comments

This sequence is equivalent to F(n)+ 6 or 2^(2^n)+ 1 + 6. This sequence does not appear to have any special divisibility properties. Fermat numbers of order 5 which are found in A063486, have the divisibility property if n is even, then 7 divides F(n,5). After the first 2 terms the ending digit is the same for all F(n,m) and is (6+m) mod 10.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..11
• Tigran Hakobyan, On the unboundedness of common divisors of distinct terms of the sequence a(n)=2^2^n+d for d>1, arXiv:1601.04946 [math.NT], 2016.

Crossrefs

Cf. A063486, A130729.

Programs

Magma

[2^(2^n)+7: n in [0..11]]; // Vincenzo Librandi, Jan 09 2013

Mathematica

Table[(2^(2^n) + 7), {n, 0, 15}] (* Vincenzo Librandi, Jan 09 2013 *)

PARI

fplusm(n,m)= { local(x,y); for(x=0,n, y=2^(2^x)+m; print1(y",") ) }

Formula

F(n,m): The n-th Fermat number of order m = 2^(2^n)+ m. The traditional Fermat numbers are F(n,1) or Fermat numbers of order 1 in this nomenclature.