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

3,1

Links

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

Formula

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A061419 A130732 A018135 * A301750 A086676 A055804

Adjacent sequences: A065432 A065433 A065434 * A065436 A065437 A065438

Keyword

nonn,easy,nice

Author

Bodo Zinser, Nov 17 2001

Extensions

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

Definition corrected by Harry J. Smith, Oct 18 2009

Status

approved