

A176352


Order the positive rationals by numerator+denominator, then by numerator. a(n+1) = a(n)*r, where r is the first unused positive rational that makes a(n+1) an integer not already in the sequence.


5



1, 2, 6, 3, 12, 4, 20, 5, 30, 45, 9, 15, 10, 25, 175, 70, 42, 7, 56, 8, 28, 21, 49, 14, 126, 168, 210, 90, 72, 16, 160, 60, 50, 225, 270, 27, 297, 33, 88, 11, 132, 231, 165, 264, 24, 54, 63, 36, 120, 75, 105, 189, 84, 462, 396, 108, 1404, 117, 65, 910, 273, 1001, 182, 13
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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.


LINKS



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(#v1, 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/(nk))); 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[i1]*pend[k];
if(denominator(try)==1&!invecn(v, i1, 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 !! (n1)
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


CROSSREFS



KEYWORD

nice,nonn


AUTHOR



EXTENSIONS



STATUS

approved



