OFFSET
0,1
COMMENTS
There appears to be no divisibility rule for this sequence.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 0..9
Anders Björn and Hans Riesel, Factors of Generalized Fermat Numbers, Mathematics of Computation, Vol. 67, No. 221, Jan., 1998, pp. 441-446.
OEIS Wiki, Generalized Fermat numbers
FORMULA
a(0) = 15, a(n) = (a(n-1)-1)^2 + 1, n >= 1.
a(n) = 13*a(n-1)*a(n-2)*...*a(1)*a(0) + 2, n >= 0, where for n = 0, we get 13*(empty product, i.e., 1)+ 2 = 15 = a(0). This implies that the terms, all odd, are pairwise coprime. - Daniel Forgues, Jun 20 2011
EXAMPLE
a(0) = 14^1+1 = 15 = 13*(1)+2 = 13(empty product)+2.
a(1) = 14^2+1 = 197 = 13*(15)+2.
a(2) = 14^4+1 = 38417 = 13*(15*197)+2.
a(3) = 14^8+1 = 1475789057 = 13*(15*197*38417)+2.
a(4) = 14^16+1 = 2177953337809371137 = 13*(15*197*38417*1475789057)+2.
a(5) = 14^32+1 = 4743480741674980702700443299789930497 = 13*(15*197*38417*1475789057*2177953337809371137)+2.
MATHEMATICA
Table[14^2^n+1, {n, 0, 7}] (* Harvey P. Dale, Jun 10 2023 *)
PROG
(PARI) g(a, n) = if(a%2, b=2, b=1); for(x=0, n, y=a^(2^x)+b; print1(y", "))
(Magma) [14^(2^n) + 1: n in [0..8]]; // Vincenzo Librandi, Jun 20 2011
(PARI) a(n)=14^(2^n)+1 \\ Charles R Greathouse IV, Jul 29 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, Dec 08 2008
STATUS
approved