A088492 a(2n+1)=2n+1, a(2n) = floor(2*n/A005185(n)), a weighted inverse of Hofstadter's Q-sequence.

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

Offset

2,1

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.

Links

Table of n, a(n) for n=2..87.

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}]

Crossrefs

Cf. A005185.

Sequence in context: A330750 A346099 A345941 * A345931 A025492 A322445

Adjacent sequences: A088489 A088490 A088491 * A088493 A088494 A088495

Keyword

nonn

Author

Roger L. Bagula, Nov 10 2003

Extensions

Definition replaced and comment added - R. J. Mathar, Dec 08 2010

Status

approved