OFFSET
1,1
COMMENTS
The left point (x,y) of intersection of quadratic fits of log(a(n)) and log(A191304(n+1)) is about (-1, 0).
a(n+1) < 2 a(n) for all n, and lim_{n->inf} a(n+1)/a(n) = 2.
With A167168(1)=3 and s_1 = {3,5,11,23,...}, p_(a(n)) = s_1(n+1) in a two-index notation for every prime p_i for i > 1 based on Shevelev's equivalence classes of Rowland-like prime sequence recurrences. These equivalence classes {s_n(k)} were defined by Shevelev, see Crossrefs.
FORMULA
a(n) = pi(A191304(n+1)).
(4/5)^2 (n - 1) < log(a(n)) < (4/5)^2 (n + 1), for at least n < 46.
MATHEMATICA
Rest@ PrimePi@ Union@ FoldList[Max, 1, Rest@ # - Most@ #] &@ FoldList[#1 + GCD[#2, #1] &, 7, Range[2, 10^7]] (* after Michael De Vlieger, Aug 19 2017, after Robert G. Wilson v at A132199 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ralf Steiner, Aug 19 2017
STATUS
approved