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A126604
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a(1) = 4; a(2) = 3; for n > 2, a(n) = a(n-1)^2 + a(n-1) - 1.
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1
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OFFSET
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1,1
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COMMENTS
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a(n) = -1 + Product_{k=1..n-1} a(k) for n > 1.
Sequence is a variant of A005267 (start values 3 and 2, offset 0). Both sequences have the same recursion formulas and both are infinite coprime sequences; a(n) has digital root 2 for odd n and 5 for even n, n > 2.
a(2) to a(6) are prime, a(1) and a(7) to a(10) are composite, a(2) to a(10) are squarefree.
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LINKS
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EXAMPLE
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a(3) = 3^2 + 3 - 1 = 11, a(4) = 11^2 + 11 - 1 = 131.
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MAPLE
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a[1]:=1: a[2]:=3: for n from 3 to 10 do a[n]:=a[n-1]^2+a[n-1]-1 od: seq(a[n], n=1..10); # Emeric Deutsch, Jan 09 2007
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MATHEMATICA
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Join[{4}, NestList[#^2+#-1&, 3, 10]] (* Harvey P. Dale, Jul 24 2012 *)
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PROG
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(PARI) 1. {print1(4, ", ", a=3, ", "); for(n=1, 8, print1(a=a^2+a-1, ", "))}
2. {m=10; v=vector(m); print1(v[1]=4, ", "); for(n=2, m, print1(v[n]=-1+prod(k=1, n-1, v[k]), ", "))} \\ Klaus Brockhaus, Jan 09 2007
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CROSSREFS
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KEYWORD
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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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