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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 (list; graph; refs; listen; history; text; internal format)
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

This ordering of the rationals is A038566/A020653.

Cf. A002487.

Sequence in context: A304752 A113552 A282291 * A064736 A303751 A304531

Adjacent sequences:  A176349 A176350 A176351 * A176353 A176354 A176355

KEYWORD

nice,nonn

AUTHOR

Franklin T. Adams-Watters, Apr 15 2010

EXTENSIONS

Definition stated more precisely by Reinhard Zumkeller, Oct 30 2012

STATUS

approved

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Last modified September 20 13:56 EDT 2021. Contains 347586 sequences. (Running on oeis4.)