OFFSET
1,2
COMMENTS
All consecutive quadruples are pairwise coprime. Multiples of 2 occur when n=2 mod 4, multiples of 3 when n=3 mod 4, multiples of 5 when n=4 mod 7, multiples of 7 when n=10 mod 14, multiples of 9 when n=7 or 11 mod 24, multiples of 10 when n=18 mod 28. Multiples of 4, 6 and 8 never occur.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..19
FORMULA
Lim_{n->infinity} a(n+1)/a(n)^phi = 1, where phi is the golden ratio (1+sqrt(5))/2 = A001622. - Benoit Cloitre, Sep 26 2002
From Jon E. Schoenfield, May 13 2019: (Start)
It appears that, for n >= 2,
a(n) = ceiling(e^(c*phi^n - d/(-phi)^n))
where
phi = (1 + sqrt(5))/2
c = 0.230193077518834725477008740044380256486365499661...
d = 0.067704372842879037264190305626317036100889750046...
(End)
EXAMPLE
a(6) = a(5)*a(4) - a(3) = 13*5 - 3 = 62.
MATHEMATICA
nxt[{a_, b_, c_}]:={b, c, b*c-a}; NestList[nxt, {1, 2, 3}, 15][[All, 1]] (* Harvey P. Dale, Jan 21 2023 *)
PROG
(Haskell)
a074394 n = a074394_list !! (n-1)
a074394_list = 1 : 2 : 3 : zipWith (-)
(tail $ zipWith (*) (tail a074394_list) a074394_list) a074394_list
-- Reinhard Zumkeller, Mar 25 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Sep 24 2002
STATUS
approved