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 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 A353383 A097274 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

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Last modified December 10 01:39 EST 2022. Contains 358711 sequences. (Running on oeis4.)