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A117385 Positive integers, each occurring twice in the sequence, such that a(n) = a(k) when n+k = 5*a(n), starting with a(1)=1 and filling the next vacant position with the smallest unused number. 3

%I

%S 1,2,3,1,4,5,6,2,7,8,9,3,10,11,4,12,13,14,5,15,16,17,6,18,19,7,20,21,

%T 22,8,23,24,25,9,26,27,10,28,29,30,11,31,32,12,33,34,35,13,36,37,38,

%U 14,39,40,15,41,42,43,16,44,45,46,17,47,48,18,49,50,51,19,52,53,20,54,55,56

%N Positive integers, each occurring twice in the sequence, such that a(n) = a(k) when n+k = 5*a(n), starting with a(1)=1 and filling the next vacant position with the smallest unused number.

%F a(5*a(n)-n) = a(n). Conjecture: Lim_inf a(n)/n = (5-sqrt(5))/10; Lim_sup a(n)/n = (5+sqrt(5))/10.

%o (PARI) {a(n)=local(A=vector(n),m=1); for(k=1,n,if(A[k]==0,A[k]=m;if(5*m-k<=#A,A[5*m-k]=m);m+=1));A[n]}

%Y Cf. A117384 (a(4*a(n)-n)=a(n)), A117386 (a(6*a(n)-n)=a(n)).

%K nonn

%O 1,2

%A _Paul D. Hanna_, Mar 11 2006

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Last modified June 21 17:22 EDT 2021. Contains 345365 sequences. (Running on oeis4.)