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A199592 Generalized Fermat numbers: 11^(2^n) + 1, n >= 0. 12
12, 122, 14642, 214358882, 45949729863572162, 2111377674535255285545615254209922, 4457915684525902395869512133369841539490161434991526715513934826242 (list; graph; refs; listen; history; text; internal format)
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.

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

Cf. A059919, A199591, A078303, A078304, A152581, A080176, A152585.

Sequence in context: A132927 A113574 A255307 * A285807 A078189 A278982

Adjacent sequences:  A199589 A199590 A199591 * A199593 A199594 A199595

KEYWORD

easy,nonn

AUTHOR

Arkadiusz Wesolowski, Nov 08 2011

STATUS

approved

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Last modified October 19 03:34 EDT 2019. Contains 328211 sequences. (Running on oeis4.)