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A080176
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Generalized Fermat numbers: 10^(2^n) + 1, n >= 0.
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6
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OFFSET
| 0,1
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COMMENTS
| As for standard Fermat numbers 2^(2^n) + 1, a number (2b)^m + 1 (with b > 1) can only be prime if m is a power of 2. On the other hand, out of the first 12 base-10 Fermat numbers, only the first two are primes.
Also, binary representation of Fermat numbers (in decimal, see A000215.)
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..12
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
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FORMULA
| a(0) = 11; a(n) = (a(n-1)-1)^2 + 1.
a(n) = 9*a(n-1)*a(n-2)*...*a(1)*a(0) + 2, n >= 0, where for n = 0, we get 9*(empty product, i.e. 1)+ 2 = 11 = a(0). - Daniel Forgues, June 20 2011
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EXAMPLE
| a(0) = 10^1+1 = 11 = 9*(1)+2 = 9*(empty product)+2;
a(1) = 10^2+1 = 101 = 9*(11)+2;
a(2) = 10^4+1 = 10001 = 9*(11*101)+2;
a(3) = 10^8+1 = 100000001 = 9*(11*101*10001)+2;
a(4) = 10^16+1 = 10000000000000001 = 9*(11*101*10001*100000001)+2;
a(5) = 10^32+1 = 100000000000000000000000000000001 = 9*(11*101*10001*100000001*10000000000000001)+2;
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PROG
| (MAGMA) [10^(2^n) + 1: n in [0..8]]; // Vincenzo Librandi, Jun 20 2011
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CROSSREFS
| Cf. A000215, A019434, A080174, A080175.
Sequence in context: A052075 A070854 A075767 * A064490 A080439 A098153
Adjacent sequences: A080173 A080174 A080175 * A080177 A080178 A080179
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KEYWORD
| easy,nonn
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AUTHOR
| Jens Voss (jens(AT)voss-ahrensburg.de), Feb 04 2003
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EXTENSIONS
| Edited by Daniel Forgues (kephalopod(AT)gmail.com), Jun 19 2011
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