OFFSET
1,2
COMMENTS
More generally let (x,y,z) be 3 positive integers and a(n) be the sequence a(1)=x, a(n) = a(n-1) + y if n is already in the sequence, a(n) = a(n-1) + z otherwise. Then it seems that a(n) is asymptotic to r*n where r is the largest positive root of q^2 = z*q + z - y.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.
FORMULA
a(n) = ceiling((1+sqrt(2))*(n-1)+C) where C = 1/(2+sqrt(2)) = 0.292893218813...
EXAMPLE
a(6)=13 hence a(13) = a(12) + 3 = 27 + 3 = 30.
MAPLE
A064437:= n -> ceil((1+sqrt(2))*(n-1)+1/(2+sqrt(2))):
seq(A064437(n), n=1..100); # Robert Israel, May 19 2014
MATHEMATICA
a[1] = 1; a[n_] := a[n] = a[n-1] + If[MemberQ[Array[a, n-1], n], 3, 2];
Array[a, 100] (* Jean-François Alcover, Aug 01 2018 *)
PROG
(PARI) an=vector(100); an[1]=1; a(n)=if(n<0, 0, an[n]);
x=1; y=3; z=2; an[1]=x; for(n=2, 100, an[n]=if(setsearch(Set(vector(n- 1, i, a(i))), n), a(n-1)+y, a(n-1)+z));
an
(Haskell)
a064437 n = a064437_list !! (n-1)
a064437_list = 1 : f 2 [1] where
f x zs@(z:_) = y : f (x + 1) (y : zs) where
y = if x `elem` zs then z + 3 else z + 2
-- Reinhard Zumkeller, Sep 26 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Feb 14 2003
STATUS
approved