login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A160256 a(1)=1, a(2)=2. For n >=3, a(n) = the smallest positive integer not occurring earlier in the sequence such that a(n)*a(n-1)/a(n-2) is an integer. 8
1, 2, 3, 4, 6, 8, 9, 16, 18, 24, 12, 10, 30, 5, 36, 15, 48, 20, 60, 7, 120, 14, 180, 21, 240, 28, 300, 35, 360, 42, 420, 11, 840, 22, 1260, 33, 1680, 44, 2100, 55, 2520, 66, 2940, 77, 3360, 88, 3780, 110, 378, 165, 126, 220, 63, 440, 189, 880, 567, 1760 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Is this sequence a permutation of the positive integers?

a(n+2)*a(n+1)/a(n) = A160257(n).

From Alois P. Heinz, May 07 2009: (Start)

After computing about 10^7 elements of A160256 we have

a(10000000) = 2099597439752627193722111679586865799879114417

a(10000001) = 992131130100042530286371815859160

Largest element so far:

a(8968546) = 24941014474345046106920043019655502800839523254002490663461\

524119982890708516899294655028121578883343551450916846444559467340663409\

549447588184641816

Still missing:

19, 23, 27, 29, 31, 32, 37, 38, 41, 43, 45, 46, 47, 53, 54, 57, 58, 59,

61, 62, 64, 67, 69, 71, 72, 73, 74, 76, 79, 81, 82, 83, 86, 87, 89, 90,

92, 93, 94, 95, 96, 97, 101, 103, 105, 106, 107, 108, 109, 111, 112, 113,

114, 115, 116, 118, 122, 123, 124, 125, 127, 128, 129, 131, 133, 134, ...

Primes in sequence so far:

2, 3, 5, 7, 11, 13, 17

The sequence consists of two subsequences, even (=red) and odd (=blue), see plot. (End)

a(n) is the least multiple of a(n-2)/gcd(a(n-1),a(n-2)) that has not previously occurred. - Thomas Ordowski, Jul 15 2015

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..130000

Alois P. Heinz, Color plot of first 600 terms

MAPLE

b:= proc(n) option remember; false end:

a:= proc(n) option remember; local k, m;

      if n<3 then b(n):=true; n

    else m:= denom(a(n-1)/a(n-2));

         for k from m by m while b(k) do od;

         b(k):= true; k

      fi

    end:

seq(a(n), n=1..100); # Alois P. Heinz, May 16 2009

MATHEMATICA

f[s_List] := Block[{k = 1, m = Denominator[ s[[ -1]]/s[[ -2]]]}, While[ MemberQ[s, k*m] || Mod[k*m*s[[ -1]], s[[ -2]]] != 0, k++ ]; Append[s, k*m]]; Nest[f, {1, 2}, 56] (* Robert G. Wilson v, May 17 2009 *)

PROG

(PARI)

LQ(nMax)={my(a1=1, a2=1, L=1/*least unseen number*/, S=[]/*used numbers above L*/);

while(1, /*cleanup*/ while( setsearch(S, L), S=setminus(S, Set(L)); L++);

/*search*/ for(a=L, nMax, a*a2%a1 & next; setsearch(S, a) & next;

print1(a", "); a1=a2; S=setunion(S, Set(a2=a)); next(2)); return(L))} \\ M. F. Hasler, May 06 2009

(PARI) L=10^4; a=vector(L); b=[1, 2]; a[1]=1; a[2]=2; sb=2; P2=2; pending=[]; sp=0; for(n=3, L, if(issquare(n), b=vecsort(concat(b, pending)); sb=n-1; while(sb>=2*P2, P2*=2); sp=0; pending=[]); c=a[n-2]/gcd(a[n-2], a[n-1]); u=0; while(1, u+=c; found=0; s=0; pow2=P2; while(pow2, s2=s+pow2; if((s2<=sb)&&(b[s2]<=u), s=s2); pow2\=2); if((s>0)&&(b[s]==u), found=1, for(i=1, sp, if(pending[i]==u, found=1; break))); if(found==0, break)); a[n]=u; pending=concat(pending, u); sp++); a \\ Robert Gerbicz, May 16 2009]

(Haskell)

import Data.List (delete)

a160256 n = a160256_list !! (n-1)

a160256_list = 1 : 2 : f 1 2 [3..] where

   f u v ws = g ws where

     g (x:xs) | mod (x * v) u == 0 = x : f v x (delete x ws)

              | otherwise          = g xs

-- Reinhard Zumkeller, Jan 31 2014

(Python)

from __future__ import division

from fractions import gcd

A160256_list, l1, l2, m, b = [1, 2], 2, 1, 1, {1, 2}

for _ in range(10**3):

....i = m

....while True:

........if not i in b:

............A160256_list.append(i)

............l1, l2, m = i, l1, l1//gcd(l1, i)

............b.add(i)

............break

........i += m # Chai Wah Wu, Dec 09 2014

CROSSREFS

Cf. A075075, A160257, A151413, A160218, A151546, A064413.

For records see A151545, A151547.

Sequence in context: A073667 A326497 A325046 * A151545 A097274 A322572

Adjacent sequences:  A160253 A160254 A160255 * A160257 A160258 A160259

KEYWORD

nonn,look

AUTHOR

Leroy Quet, May 06 2009

EXTENSIONS

More terms from M. F. Hasler, May 06 2009

Edited by N. J. A. Sloane, May 16 2009

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 10 04:15 EST 2019. Contains 329885 sequences. (Running on oeis4.)