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A152587
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Generalized Fermat numbers: a(n) = 14^(2^n) + 1.
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2
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OFFSET
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0,1
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COMMENTS
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There appears to be no divisibility rule for this sequence.
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LINKS
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FORMULA
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a(0) = 15, a(n) = (a(n-1)-1)^2 + 1, n >= 1.
a(n) = 13*a(n-1)*a(n-2)*...*a(1)*a(0) + 2, n >= 0, where for n = 0, we get 13*(empty product, i.e., 1)+ 2 = 15 = a(0). This implies that the terms, all odd, are pairwise coprime. - Daniel Forgues, Jun 20 2011
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EXAMPLE
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a(0) = 14^1+1 = 15 = 13*(1)+2 = 13(empty product)+2.
a(1) = 14^2+1 = 197 = 13*(15)+2.
a(2) = 14^4+1 = 38417 = 13*(15*197)+2.
a(3) = 14^8+1 = 1475789057 = 13*(15*197*38417)+2.
a(4) = 14^16+1 = 2177953337809371137 = 13*(15*197*38417*1475789057)+2.
a(5) = 14^32+1 = 4743480741674980702700443299789930497 = 13*(15*197*38417*1475789057*2177953337809371137)+2.
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MATHEMATICA
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PROG
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(PARI) g(a, n) = if(a%2, b=2, b=1); for(x=0, n, y=a^(2^x)+b; print1(y", "))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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