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Search: id:A117384
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| A117384 |
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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. |
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6
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Positions where n occurs are A001614(n) and 4*n-A001614(n), where A001614 is the Connell sequence: 1 odd, 2 even, 3 odd, ...
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FORMULA
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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.
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EXAMPLE
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9 first appears at position: A001614(9) = 14;
9 next appears at position: 4*9 - A001614(9) = 22.
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PROGRAM
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(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]}
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CROSSREFS
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Cf. A117385 (a(5*a(n)-n)=a(n)), A117386 (a(6*a(n)-n)=a(n)).
Cf. A001614 (Connell sequence).
Adjacent sequences: A117381 A117382 A117383 this_sequence A117385 A117386 A117387
Sequence in context: A131987 A120874 A112382 this_sequence A125160 A009947 A026249
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 11 2006
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