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 A109852 a(1)=1; a(2) = 2; for n >= 1 and 1 <= k < 2^n, a(2^n+k) is the least multiple of a(2^n-k) not included earlier and a(2^n) is the least number not included earlier. 3
 1, 2, 3, 4, 6, 8, 5, 7, 10, 16, 12, 20, 9, 14, 11, 13, 22, 28, 18, 40, 24, 32, 30, 21, 15, 48, 36, 44, 27, 26, 17, 19, 34, 52, 54, 88, 72, 96, 45, 42, 60, 64, 120, 80, 90, 56, 66, 39, 33, 70, 63, 100, 84, 112, 50, 35, 25, 104, 78, 68, 51, 38, 23, 29, 46, 76, 102, 136, 156, 208 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Every number appears and no number is repeated. Conjecture: a(2^n) is prime if n is not 0 nor 2. Conjecture: for n>2, every odd prime >4 is encountered in order at a(2^n-1), a(2^n). - Bill McEachen, May 06 2014 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 EXAMPLE a(8) = 7 as the least number not included earlier. a(9) = 2*a(8) = 2*5=10, a(10) = 2*a(6) = 16, a(11) = 2*a(5) = 12, a(12)= 5*a(4) = 20 as 8, 12 and 16 have already been included. MAPLE did := [1]; lef := []; for n from 2 to 1000 do lef := [op(lef), n]; od : tak2n := proc(n2n) local i; global lef; i := op(1, lef); lef := subsop(1=NULL, lef); RETURN(i); end : tak := proc(n2n) local noffs, need, lefi, nindx, aa, mul; global lef, did; for noffs from -1 to -n2n+1 by -1 do nindx := n2n+noffs; aa := did[nindx]; for mul from 2 to 10000 do need := aa*mul; if member(need, lef, 'lefi') = true then break; fi; od : lef := subsop(lefi=NULL, lef); printf("%d, ", need); did := [op(did), need]; od : RETURN(ret); end : printf("1, "); for bas from 1 to 5 do nstrt := 2^bas; a := tak2n(nstrt); printf("%d, ", a); did := [op(did), a]; tak(nstrt); od : # R. J. Mathar, Mar 27 2006 # second Maple program: ina:= proc(n) evalb(n<3) end: a:= proc(n) option remember; local k, i, t;       if n<3 then n       else a(n-1);            k:= n-2^ilog2(n);            t:= `if`(k=0, 1, a(n-2*k));            for i from 2*t by t while ina(i) do od;            ina(i):= true; i       fi     end: seq(a(n), n=1..70);  # Alois P. Heinz, Feb 07 2011 MATHEMATICA f[s_] := Block[{k = 2, len = Length@s}, exp = Ceiling[Log[2, len]]; m = s[[2^exp - len + 1]]; While[MemberQ[s, k*m], k++ ]; Append[s, k*m]]; Rest@Nest[f, {1, 1}, 70] (* the programming trick is to set a(0)=1 *) (* Robert G. Wilson v *) CROSSREFS Cf. A109853, A308301 (inverse). Sequence in context: A339361 A166310 A293030 * A083197 A235262 A245704 Adjacent sequences:  A109849 A109850 A109851 * A109853 A109854 A109855 KEYWORD nonn,look AUTHOR Amarnath Murthy, Jul 07 2005 EXTENSIONS More terms from R. J. Mathar, Mar 27 2006 Edited and extended by Robert G. Wilson v, Jun 14 2006 STATUS approved

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Last modified December 5 08:36 EST 2021. Contains 349543 sequences. (Running on oeis4.)