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A102847
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a(0)=1, a(n) = a(n-1)*a(n-1) + 2.
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2
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OFFSET
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0,2
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COMMENTS
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The Mandelbrot-process is z:=z*z+c, where z and c is complex. In our case c=2 and the initial z is 1. The process is very quickly increasing.
Prime for a(1)=3, a(2)=11, a(4)=15131; semiprime for a(3) = 123 = 3 * 41, a(5) = 228947163 = 3 * 76315721. a(6), added by Jonathan Vos Post, has 4 prime factors. a(7) = 41 * 811^2 * 106693969 * 317171188688357726699 * 8272236925540996054440172449761. When is the next prime in the sequence? - Jonathan Vos Post, Feb 28 2005
Composite for a(8), a(9), ..., a(19). a(20) is roughly 2^909982 and its primality is unknown. - Russ Cox, Apr 02 2006
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LINKS
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FORMULA
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a(n) ~ c^(2^n), where c = 1.8249111600523655937123650418390169034... - Vaclav Kotesovec, Sep 20 2013
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EXAMPLE
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a(2)=11, a(3)=11*11+2=123.
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MAPLE
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a[0]:=1: for n from 1 to 10 do a[n]:=a[n-1]^2+2 od: seq(a[n], n=0..9); # Emeric Deutsch
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MATHEMATICA
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PROG
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(PARI) a(n)=if(n<1, n==0, 2+a(n-1)^2) /* Michael Somos, Mar 25 2006 */
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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