The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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#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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 10 07:34 EDT 2023. Contains 363195 sequences. (Running on oeis4.)