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A088492
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a(2n+1)=2n+1, a(2n) = floor(2*n/A005185(n)), a weighted inverse of Hofstadter's Q-sequence.
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2, 3, 4, 5, 3, 7, 2, 9, 3, 11, 3, 13, 2, 15, 3, 17, 3, 19, 3, 21, 3, 23, 3, 25, 3, 27, 3, 29, 3, 31, 3, 33, 3, 35, 3, 37, 3, 39, 3, 41, 3, 43, 3, 45, 3, 47, 3, 49, 3, 51, 3, 53, 3, 55, 3, 57, 3, 59, 3, 61, 3, 63, 3, 65, 3, 67, 3, 69, 3, 71, 3, 73, 3, 75, 3, 77, 3, 79, 3, 81, 3, 83, 3, 85, 3, 87
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| Define a sequence of partial products of Hofstadters Q-sequence, H(n) = prod_{i=1..n} A005185(i) = 1, 1, 2, 6, 18, 72, 360, 1800,.. for n>=1 (which differs from A004395).
The original definition was equivalent to a(n) = [n *H([(n-1)/2])/H([n/2])] where [..] is the floor function.
A consequence of this construction is a(2n+1)=2n+1 at the odd indices. At the even indices, a(2*n) = [2*n*H(n-1)/H(n)] = [2*n/A005185(n)], which is used to simplify the definition.
a(2n)=3 for 8<=n<=48. The first 5 at an even index occurs at a(2*193)=5.
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MATHEMATICA
| Hofstadter[n_Integer?Positive] := Hofstadter[n] = Hofstadter[n - Hofstadter[n-1]] + Hofstadter[n - Hofstadter[n-2]] Hofstadter[1] = Hofstadter[2] = 1 p[n_]=n!/Product[Hofstadter[i], {i, 1, Floor[n/2]}] digits=200 a0=Table[Floor[p[n]/p[n-1]], {n, 2, digits}]
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CROSSREFS
| Cf. A005185.
Sequence in context: A127064 A117607 A194551 * A025492 A077004 A064760
Adjacent sequences: A088489 A088490 A088491 * A088493 A088494 A088495
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 10 2003
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EXTENSIONS
| Definition replaced and comment added - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 08 2010
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