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

2, 3, 5, 8, 12, 18, 28, 40, 60, 96, 148, 228, 366, 586, 936, 1506, 2428, 3922, 6342, 10256, 16590, 26826, 43394, 70212, 113598, 183798, 297388, 481174, 778548, 1259712, 2038242, 3297918, 5336130, 8634042, 13970112, 22604076, 36574162

Offset: 3

Author

Bodo Zinser, Nov 17 2001

Keywords

• nonn
• easy
• nice

Examples

			a(9) = 28 because 11+17 = 28 and 11 largest prime <= a(7) = 12 and 17 is largest prime <= a(8) = 18
		

Links

• Harry J. Smith, Table of n, a(n) for n = 3..300

Crossrefs

Cf. A055500, A000040, A000045, A007917, A055500.

Programs

Haskell

a065435 n = a065435_list !! (n-3)
a065435_list = 2 : 3 : zipWith (+) xs (tail xs) where
               xs = map (a007917 . fromInteger) a065435_list
-- Reinhard Zumkeller, Aug 10 2012

Mathematica

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} ]
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 *)

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

Formula

a(n) = A007917(a(n-2)) + A007917(a(n-1)). - Jonathan Vos Post, Jul 10 2008

Extensions

More terms from Robert G. Wilson v, Nov 19 2001

Definition corrected by Harry J. Smith, Oct 18 2009