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A117805
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Start with 3. Square the previous term and subtract it.
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3
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3, 6, 30, 870, 756030, 571580604870, 326704387862983487112030, 106735757048926752040856495274871386126283608870, 11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068030
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OFFSET
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0,1
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COMMENTS
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The next term is too large to include.
For any a(0) > 2, the sequence a(n) = a(n-1) * (a(n-1) - 1) gives a constructive proof that there exists integers with at least n + 1 distinct prime factors, e.g., a(n). As a corollary, this gives a constructive proof of Euclid's theorem stating that there are an infinity of primes. - Daniel Forgues, Mar 03 2017
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LINKS
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FORMULA
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a(0) = 3, a(n) = (a(n-1))^2 - a(n-1).
a(n) ~ c^(2^n), where c = 2.330283023986140936420341573975137247354077600883596774023675490739568138... . - Vaclav Kotesovec, Dec 17 2014
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EXAMPLE
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Start with 3; 3^2 - 3 = 6; 6^2 - 6 = 30; etc.
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MAPLE
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f:=proc(n) option remember; if n=0 then RETURN(3); else RETURN(f(n-1)^2-f(n-1)); fi; end;
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MATHEMATICA
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RecurrenceTable[{a[0]==3, a[n]==a[n-1]*(a[n-1] - 1)}, a, {n, 0, 10}] (* Vaclav Kotesovec, Dec 17 2014 *)
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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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STATUS
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approved
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