OFFSET
1,2
COMMENTS
It appears that this sequence is a permutation of the positive integers.
It appears that every positive rational except 1 occurs as the ratio of consecutive terms.
A218454 gives smallest numbers m such that a(m)=n; a(A176352(n))=n. - Reinhard Zumkeller, Oct 30 2012
A218535(n) = gcd(a(n),a(n+1)); A218533(n)/A218534(n) = a(n)/a(n+1). - Reinhard Zumkeller, Nov 10 2012
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
EXAMPLE
After a(6)=4, we have used ratios 1/2, 2, 1/3, and 3. 1/4 would give 1, which is already used. 2/3 would give 8/3, not an integer; 3/2 would give 6, already used; and ratio 4 is already used. 1/5 would not produce an integer; next is 5, giving a(7) = 4*5 = 20.
PROG
(PARI) copywo(v, k)=vector(#v-1, i, v[if(i<k, i, i+1)])
rprat(n)=local(v, i); v=vector(eulerphi(n)); i=0; for(k=1, n, if(gcd(k, n)==1, v[i++ ]=k/(n-k))); v
invecn(v, n, x)=for(k=1, n, if(v[k]==x, return(1))); 0
al(n)={local(v, pend, last, k, try);
v=vector(n); v[1]=1; pend=[]; last=2;
for(i=2, n,
k=1; while(1,
if(k>#pend, pend=concat(pend, rprat(last++)));
try=v[i-1]*pend[k];
if(denominator(try)==1&!invecn(v, i-1, try),
pend=copywo(pend, k); v[i]=try; break);
k++)); v}
(Haskell)
import Data.Ratio ((%), numerator, denominator)
import Data.List (delete)
import Data.Set (singleton, insert, member)
a176352 n = a176352_list !! (n-1)
a176352_list = 1 : f 1 (singleton 1) (concat $ drop 2 $
zipWith (zipWith (%)) a038566_tabf $ map reverse a038566_tabf)
where f x ws qs = h qs
where h (r:rs) | denominator y /= 1 || v `member` ws = h rs
| otherwise = v : f y (insert v ws) (delete r qs)
where v = numerator y; y = x * r
-- Reinhard Zumkeller, Oct 30 2012
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
Franklin T. Adams-Watters, Apr 15 2010
EXTENSIONS
Definition stated more precisely by Reinhard Zumkeller, Oct 30 2012
STATUS
approved