A218534 -id:A218534 - cp's OEIS frontend

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.

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

Offset: 1

Franklin T. Adams-Watters, Apr 15 2010

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

			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.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

This ordering of the rationals is A038566/A020653.

Cf. A002487.

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

copywo(v,k)=vector(#v-1,i,v[if(i#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}

Definition stated more precisely by Reinhard Zumkeller, Oct 30 2012

A218535 Greatest common divisor of consecutive terms in A176352.

Original entry on oeis.org

1, 2, 3, 3, 4, 4, 5, 5, 15, 9, 3, 5, 5, 25, 35, 14, 7, 7, 8, 4, 7, 7, 7, 14, 42, 42, 30, 18, 8, 16, 20, 10, 25, 45, 27, 27, 33, 11, 11, 11, 33, 33, 33, 24, 6, 9, 9, 12, 15, 15, 21, 21, 42, 66, 36, 108, 117, 13, 65, 91, 91, 91, 13, 13, 39, 33, 22, 22, 11, 13

Offset: 1

Reinhard Zumkeller, Nov 10 2012

nonn

a(n) = gcd(A176352(n),A176352(n+1)).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A176352, A218533, A218534.

import Data.Ratio ((%), numerator, denominator)
a218535 n = a218535_list !! (n-1)
a218535_list = zipWith gcd a176352_list $ tail a176352_list
-- .

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

PARI

Extensions