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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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1
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1, 3, 11, 123, 15131, 228947163, 52416803445748571, 2747521283470239265968814548542043, 7548873203121950871924356140057489033996373873303512592376938613851
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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 (jvospost3(AT)gmail.com), Feb 28 2005
Composite for a(8), a(9), ..., a(19). a(20) is roughly 2^909982 and its primality is unknown. - Russ Cox (rsc(AT)swtch.com), Apr 2 2006
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EXAMPLE
| a(2)=11, a(3)=11*11+2=123
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MAPLE
| a[0]:=1: for n from 1 to 10 do a[n]:=a[n-1]^2+2 od: seq(a[n], n=0..9); (Deutsch)
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MATHEMATICA
| a[0] := 1; a[n_] := a[n - 1]^2 + 2; Table[a[n], {n, 0, 10}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 08 2006
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PROG
| (PARI) a(n)=if(n<1, n==0, 2+a(n-1)^2) /* Michael Somos Mar 25 2006 */
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CROSSREFS
| Bisection of A065653.
Sequence in context: A036930 A198085 A015047 * A113258 A113848 A201611
Adjacent sequences: A102844 A102845 A102846 * A102848 A102849 A102850
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KEYWORD
| easy,nonn
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AUTHOR
| Miklos Kristof (kristmikl(AT)freemail.hu), Feb 28 2005
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EXTENSIONS
| a(7) from Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 28 2005
a(8) from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 13 2005
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