OFFSET
0,1
LINKS
Arkadiusz Wesolowski, Table of n, a(n) for n = 0..11
Anders Björn and Hans Riesel, Factors of Generalized Fermat Numbers, Mathematics of Computation, Vol. 67, No. 221 (Jan., 1998), pp. 441-446.
Eric Weisstein's World of Mathematics, Generalized Fermat Number.
OEIS Wiki, Generalized Fermat numbers.
FORMULA
a(0) = 12; a(n) = (a(n-1)-1)^2 + 1, n >= 1.
a(0) = 12, a(1) = 122; a(n) = a(n-1) + 10*11^(2^(n-1))*Product_{i=0..n-2} a(i), n >= 2.
a(0) = 12, a(1) = 122; a(n) = a(n-1)^2 - 2*(a(n-2)-1)^2, n >= 2.
a(0) = 12; a(n) = 10*(Product_{i=0..n-1} a(i)) + 2, n >= 1.
a(n) = A152583(n) - 1.
Sum_{n>=0} 2^n/a(n) = 1/10. - Amiram Eldar, Oct 03 2022
Product_{n>=0} (1 - 1/a(n)) = 10/11. - Amiram Eldar, Dec 01 2025
EXAMPLE
a(0) = 11^(2^0) + 1 = 11^1 + 1 = 12 = 10*(2^0) + 2.
a(1) = 11^(2^1) + 1 = 11^2 + 1 = 122 = 10*(2^1*6) + 2.
a(2) = 11^(2^2) + 1 = 11^4 + 1 = 14642 = 10*(2^2*6*61) + 2.
a(3) = 11^(2^3) + 1 = 11^8 + 1 = 214358882 = 10*(2^3*6*61*7321) + 2.
a(4) = 11^(2^4) + 1 = 11^16 + 1 = 45949729863572162 = 10*(2^4*6*61*7321*107179441) + 2.
a(5) = 11^(2^5) + 1 = 11^32 + 1 = 2111377674535255285545615254209922 = 10*(2^5*6*61*7321*107179441*22974864931786081) + 2.
MATHEMATICA
Table[11^2^n + 1, {n, 0, 6}]
PROG
(Magma) [11^2^n+1 : n in [0..6]];
(PARI) for(n=0, 6, print1(11^2^n+1, ", "))
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Arkadiusz Wesolowski, Nov 08 2011
STATUS
approved