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%I #4 Mar 30 2012 18:36:56
%S 1,2,3,4,1,5,6,7,8,2,9,10,11,12,3,13,14,15,16,4,17,18,19,5,20,21,22,
%T 23,6,24,25,26,27,7,28,29,30,31,8,32,33,34,9,35,36,37,38,10,39,40,41,
%U 42,11,43,44,45,46,12,47,48,49,13,50,51,52,53,14,54,55,56,57,15,58,59,60,61
%N Positive integers, each occurring twice in the sequence, such that a(n) = a(k) when n+k = 6*a(n), starting with a(1)=1 and filling the next vacant position with the smallest unused number.
%F a(6*a(n)-n) = a(n). Conjecture: Lim_inf a(n)/n = (3-sqrt(3))/6; Lim_sup a(n)/n = (3+sqrt(3))/6.
%o (PARI) {a(n)=local(A=vector(n),m=1); for(k=1,n,if(A[k]==0,A[k]=m;if(6*m-k<=#A,A[6*m-k]=m);m+=1));A[n]}
%Y Cf. A117384 (a(4*a(n)-n)=a(n)), A117385 (a(5*a(n)-n)=a(n)).
%K nonn
%O 1,2
%A _Paul D. Hanna_, Mar 11 2006
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