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A065435 a(3) = 2, a(4) = 3; for n > 4, a(n) = {a(n-2)}+{a(n-1)}, where {a} means largest prime <= a.

%I A065435 #18 Nov 21 2013 12:47:34
%S A065435 2,3,5,8,12,18,28,40,60,96,148,228,366,586,936,1506,2428,3922,6342,
%T A065435 10256,16590,26826,43394,70212,113598,183798,297388,481174,778548,
%U A065435 1259712,2038242,3297918,5336130,8634042,13970112,22604076,36574162
%N A065435 a(3) = 2, a(4) = 3; for n > 4, a(n) = {a(n-2)}+{a(n-1)}, where {a} means largest prime <= a.
%H A065435 Harry J. Smith, <a href="/A065435/b065435.txt">Table of n, a(n) for n = 3..300</a>
%F A065435 a(n) = A007917(a(n-2)) + A007917(a(n-1)). - _Jonathan Vos Post_, Jul 10 2008
%e A065435 a(9) = 28 because 11+17 = 28 and 11 largest prime <= a(7) = 12 and 17 is largest prime <= a(8) = 18
%t A065435 PrevPrim[n_] := Block[ {k = n}, While[ !PrimeQ[k], k-- ]; Return[k]]; a[3] = 2; a[4] = 3; a[n_] := a[n] = PrevPrim[ a[n - 1]] + PrevPrim[ a[n - 2]]; Table[ a[n], {n, 3, 45} ]
%t A065435 np[n_]:=If[PrimeQ[n],n,NextPrime[n,-1]]; Transpose[NestList[{Last[#], np[Last[#]]+np[First[#]]}&,{2,3},40]][[1]] (* _Harvey P. Dale_, Oct 01 2011 *)
%o A065435 (PARI) for (n=3, 300, if (n>4, a=precprime(a2) + precprime(a1); a2=a1; a1=a, if (n==4, a=a1=3, a=a2=2)); write("b065435.txt", n, " ", a) ) \\ _Harry J. Smith_, Oct 18 2009
%o A065435 (Haskell)
%o A065435 a065435 n = a065435_list !! (n-3)
%o A065435 a065435_list = 2 : 3 : zipWith (+) xs (tail xs) where
%o A065435                xs = map (a007917 . fromInteger) a065435_list
%o A065435 -- _Reinhard Zumkeller_, Aug 10 2012
%Y A065435 Cf. A055500, A000040, A000045, A007917, A055500.
%K A065435 nonn,easy,nice
%O A065435 3,1
%A A065435 _Bodo Zinser_, Nov 17 2001
%E A065435 More terms from _Robert G. Wilson v_, Nov 19 2001
%E A065435 Definition corrected by _Harry J. Smith_, Oct 18 2009