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%I #22 Nov 23 2020 14:20:44
%S 1,2,4,6,3,5,10,8,12,9,15,20,16,28,7,11,22,14,21,18,24,44,33,27,36,32,
%T 40,25,30,42,35,45,54,48,56,49,63,72,64,88,55,50,60,66,77,70,80,104,
%U 13,17,34,26,39,51,68,52,65,75,90,78,91,84,96,136,85,95,19
%N a(1)=1, a(2)=2; a(n+2) is the smallest number not occurring earlier such that gcd(a(n),a(n+1)) * gcd(a(n+1),a(n+2)) = a(n+1).
%C Is this a permutation of all natural numbers?
%C For n>1, gcd(a(n),a(n+1))=1 iff a(n)=prime(2k) and a(n+1)=prime(2k+1).
%H Alois P. Heinz, <a href="/A259840/b259840.txt">Table of n, a(n) for n = 1..10000</a>
%p b:= proc(n) n>2 end:
%p a:= proc(n) option remember; local k;
%p if n<3 then n else for k do if b(k) and a(n-1)
%p = igcd(a(n-2), a(n-1))*igcd(a(n-1), k) then
%p b(k):= false; return k fi od
%p fi
%p end:
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Jul 09 2015
%t a[1] = 1; a[2] = 2;
%t used = {1, 2};
%t a[n_] := a[n] = For[k = 1, True, k++, If[FreeQ[used, k], If[GCD[a[n-2], a[n-1]] GCD[a[n-1], k] == a[n-1], AppendTo[used, k]; Return[k]]]];
%t Array[a, 100] (* _Jean-François Alcover_, Nov 23 2020 *)
%K nonn,look
%O 1,2
%A _Thomas Ordowski_, Jul 06 2015
%E More terms from _Alois P. Heinz_, Jul 09 2015
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