|
|
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.
|
|
4
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Conjecture. lim a(n+1)/a(n)=phi as n goes to infinity (phi=golden ratio).
|
|
LINKS
|
|
|
FORMULA
|
|
|
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}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|