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Search: id:A002516
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| A002516 |
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Earliest sequence with a(a(n))=2n. |
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+0
11
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| 0, 3, 6, 2, 12, 7, 4, 10, 24, 11, 14, 18, 8, 15, 20, 26, 48, 19, 22, 34, 28, 23, 36, 42, 16, 27, 30, 50, 40, 31, 52, 58, 96, 35, 38, 66, 44, 39, 68, 74, 56, 43, 46, 82, 72, 47, 84, 90, 32, 51, 54, 98, 60, 55, 100, 106, 80, 59, 62, 114, 104, 63, 116, 122, 192, 67, 70, 130
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
Index entries for sequences of the a(a(n)) = 2n family
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FORMULA
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a(4n) = 2*(a(2n)), a(4n+1) = 4n+3, a(4n+2) = 2*(a(2n+1)), a(4n+3) = 8n+2. - Henry Bottomley (se16(AT)btinternet.com), Apr 27 2000
Formulae from Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 22 2004: a(n) = n + 2*A006519 if odd part of n is of form 4k+1, or 2n - 4*A006519 otherwise. a(2n) = 2a(n), a(2n+1) = 2n + 3 + (2n - 5)[n mod 2]. G.f.: sum(k>=0, 2^k*t(6t^6+t^4+2t^2+3)/(1-t^4)^2, t=x^2^k).
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PROGRAM
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(PARI) v2(n)=valuation(n, 2) a(n)=2^v2(n)*(-1+3/2*n/2^v2(n)-(-3+1/2*n/2^v2(n))*(-1)^((n/2^v2(n)-1)/2))
(PARI) a(n)=local(t): if(n<1, 0, if(n%2==0, 2*a(n/2), t=(n-1)/2:3*t+1/2-(t-5/2)*(-1)^t)) (Ralf Stephan)
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CROSSREFS
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Cf. A002517, A007379, A091067.
Sequence in context: A135598 A099506 A154204 this_sequence A073807 A090774 A147995
Adjacent sequences: A002513 A002514 A002515 this_sequence A002517 A002518 A002519
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KEYWORD
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nonn,nice
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AUTHOR
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Colin Mallows (colinm(AT)research.avayalabs.com)
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