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.

5, 7, 7, 11, 13, 19, 29, 43, 67, 107, 167, 271, 433, 701, 1129, 1823, 2939, 4759, 7691, 12437, 20123, 32537, 52631, 85121, 137723, 222841, 360551, 583351, 943871, 1527203, 2471071, 3998263, 6469303, 10467547, 16936753, 27404297, 44341027, 71745313, 116086303

Offset: 1

Author

Vladimir Shevelev, Mar 16 2013

Keywords

• nonn

Comments

Conjecture. lim a(n+1)/a(n)=phi as n goes to infinity (phi=golden ratio).

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000045, A002375, A025019, A216275.

Programs

Mathematica

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}]

Formula

a(n) = g(A216275(n+2)).