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A117384 Positive integers, each occurring twice in the sequence, such that a(n) = a(k) when n+k = 4*a(n), starting with a(1)=1 and filling the next vacant position with the smallest unused number. 5

%I

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

%T 18,13,19,14,20,15,21,22,16,23,17,24,18,25,19,26,20,27,21,28,29,22,30,

%U 23,31,24,32,25,33,26,34,27,35,28,36,37,29,38,30,39,31,40,32,41,33,42

%N Positive integers, each occurring twice in the sequence, such that a(n) = a(k) when n+k = 4*a(n), starting with a(1)=1 and filling the next vacant position with the smallest unused number.

%C Positions where n occurs are A001614(n) and 4*n-A001614(n), where A001614 is the Connell sequence: 1 odd, 2 even, 3 odd, ...

%F a(4*a(n)-n) = a(n). Limit a(n)/n = 1/2. Limit (a(n+1)-a(n))/sqrt(n) = 1.

%F a( A001614(n) ) = n; a( 4n - A001614(n) ) = n.

%e 9 first appears at position: A001614(9) = 14;

%e 9 next appears at position: 4*9 - A001614(9) = 22.

%o (PARI) {a(n)=local(A=vector(n),m=1); for(k=1,n,if(A[k]==0,A[k]=m;if(4*m-k<=#A,A[4*m-k]=m);m+=1));A[n]}

%Y Cf. A117385 (a(5*a(n)-n)=a(n)), A117386 (a(6*a(n)-n)=a(n)).

%Y Cf. A001614 (Connell sequence).

%K nonn

%O 1,2

%A _Paul D. Hanna_, Mar 11 2006

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Last modified May 11 18:05 EDT 2021. Contains 343805 sequences. (Running on oeis4.)