cp's OEIS Frontend

A216835 Fibonacci + Goldbach (dual sequence to A216275). a(1)=5, a(2)=7 and for n>=3, a(n) = g(a(n-1) + a(n-2)), where for m>=3, g(2*m) is the maximal prime p < 2*m such that 2*m - p is prime.

%I A216835 #22 Mar 27 2013 14:42:18
%S A216835 5,7,7,11,13,19,29,43,67,107,167,271,433,701,1129,1823,2939,4759,7691,
%T A216835 12437,20123,32537,52631,85121,137723,222841,360551,583351,943871,
%U A216835 1527203,2471071,3998263,6469303,10467547,16936753,27404297,44341027,71745313,116086303
%N A216835 Fibonacci + Goldbach (dual sequence to A216275). a(1)=5, a(2)=7 and for n>=3, a(n) = g(a(n-1) + a(n-2)), where for m>=3, g(2*m) is the maximal prime p < 2*m such that 2*m - p is prime.
%C A216835 Conjecture. lim a(n+1)/a(n)=phi as n goes to infinity (phi=golden ratio).
%H A216835 Peter J. C. Moses, <a href="/A216835/b216835.txt">Table of n, a(n) for n = 1..1000</a>
%F A216835 a(n) = g(A216275(n+2)).
%t A216835 a[1] = 5; a[2] = 7; g[n_] := Module[{tmp,k=1}, While[!PrimeQ[n-(tmp=NextPrime[n,-k])], k++]; tmp]; a[n_] := a[n] = g[a[n-1] + a[n-2]]; Table[a[n], {n,1,100}]
%Y A216835 Cf. A000045, A002375, A025019, A216275.
%K A216835 nonn
%O A216835 1,1
%A A216835 _Vladimir Shevelev_, Mar 16 2013