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a(1)=3; a(n>1)= greatest prime divisor of a(n-1) + n.

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`%I #11 Apr 14 2015 22:02:54
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`%S 3,5,2,3,2,2,3,11,5,5,2,7,5,19,17,11,7,5,3,23,11,11,17,41,11,37,2,5,
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`%T 17,47,13,5,19,53,11,47,7,5,11,17,29,71,19,7,13,59,53,101,5,11,31,83,
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`%U 17,71,7,7,2,5,2,31,23,17,5,23,11,11,13,3,3,73,3,5,13,29,13,89,83,23,17
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`%N a(1)=3; a(n>1)= greatest prime divisor of a(n-1) + n.
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`%C Starting with 4th term the sequence coincides with sequence with a(1)=2. Also starting with 49th term both sequence coincide with the sequence with a(1)=1! Surprisingly, the sequence with a(1)=4&5 also coincide with all above sequence starting with 49th term.
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`%H Harvey P. Dale, <a href="/A076562/b076562.txt">Table of n, a(n) for n = 1..1000</a>
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`%t nxt[{n_,a_}]:={n+1,FactorInteger[a+n+1][[-1,1]]}; Transpose[NestList[nxt,{1,3},80]][[2]] (* _Harvey P. Dale_, Apr 14 2015 *)
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`%K easy,nonn
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`%O 1,1
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`%A _Zak Seidov_, Oct 19 2002
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