OFFSET
1,2
COMMENTS
More generally for fixed r, there is a nice connection between the sequence a(1)=1, a(n) = a(n-1) + 1 if n is in the sequence, a(n) = a(n-1) + r + 1 otherwise and the so-called metafibonacci sequences. Indeed, (a(n)-n)/r is a generalized metafibonacci sequence of order r as defined in Ruskey's recent paper (reference given at A046699). - Benoit Cloitre, Feb 04 2007
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.
FORMULA
a(n) = 2n + O(1); a(2^n) = 2^(n+1). - Benoit Cloitre, Oct 12 2003
a(1) = 1, for n >= 2 a(n) = a(n + 1 - 2^floor(log(n)/log(2))) + 2*2^floor(log(n)/log(2)) - 1; (a(n) - n)/2 = A046699(n) for n >= 2. - Benoit Cloitre, Feb 04 2007
a(n) = A055938(n-1) + 2 (conjectured). - Ralf Stephan, Dec 27 2013
MATHEMATICA
l={1}; a=1; For[n=2, n<=100, If[MemberQ[l, n], a=a+1, a=a+3]; AppendTo[l, a]; n++]; l (* Indranil Ghosh, Apr 07 2017 *)
PROG
(PARI) a(n)=if(n<2, 1, a(n+1-2^floor(log(n)/log(2)))+2*2^floor(log(n)/log(2))-1) \\ Benoit Cloitre, Feb 04 2007
(Haskell)
a080578 n = a080578_list !! (n-1)
a080578_list = 1 : f 2 [1] where
f x zs@(z:_) = y : f (x + 1) (y : zs) where
y = if x `elem` zs then z + 1 else z + 3
-- Reinhard Zumkeller, Sep 26 2014
(Python)
l=[1]
a=1
for n in range(2, 101):
a += 3 if n not in l else 1
l.append(a)
print(l) # Indranil Ghosh, Apr 07 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane and Benoit Cloitre, Mar 23 2003
STATUS
approved