login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
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
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
For records see A151545, A151547.
Sequence in context: A073667 A326497 A325046 * A151545 A353383 A097274
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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 22 18:10 EST 2024. Contains 370260 sequences. (Running on oeis4.)