

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



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, 18, 13, 19, 14, 20, 15, 21, 22, 16, 23, 17, 24, 18, 25, 19, 26, 20, 27, 21, 28, 29, 22, 30, 23, 31, 24, 32, 25, 33, 26, 34, 27, 35, 28, 36, 37, 29, 38, 30, 39, 31, 40, 32, 41, 33, 42
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OFFSET

1,2


COMMENTS

Positions where n occurs are A001614(n) and 4*nA001614(n), where A001614 is the Connell sequence: 1 odd, 2 even, 3 odd, ...


LINKS

Table of n, a(n) for n=1..75.


FORMULA

a(4*a(n)n) = a(n). Limit a(n)/n = 1/2. Limit (a(n+1)a(n))/sqrt(n) = 1.
a( A001614(n) ) = n; a( 4n  A001614(n) ) = n.


EXAMPLE

9 first appears at position: A001614(9) = 14;
9 next appears at position: 4*9  A001614(9) = 22.


PROG

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


CROSSREFS

Cf. A117385 (a(5*a(n)n)=a(n)), A117386 (a(6*a(n)n)=a(n)).
Cf. A001614 (Connell sequence).
Sequence in context: A131987 A120874 A112382 * A125160 A009947 A166711
Adjacent sequences: A117381 A117382 A117383 * A117385 A117386 A117387


KEYWORD

nonn


AUTHOR

Paul D. Hanna, Mar 11 2006


STATUS

approved



