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URL: https://oeis.org/A072404

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A072404
Denominator of the Reingold-Tarjan sequence, numerator=A072403.
2
1, 3, 9, 9, 27, 27, 3, 27, 81, 81, 27, 81, 81, 9, 81, 81, 243, 243, 27, 243, 243, 81, 243, 243, 81, 243, 243, 27, 243, 243, 81, 243, 729, 729, 243, 729, 729, 81, 729, 729, 243, 729, 729, 243, 729, 729, 9, 729, 729, 243, 729, 729, 243, 729, 729, 81
OFFSET
1,2
COMMENTS
The Reingold-Tarjan sequence is based on the following function defined on even positive integers and range of the rational numbers:
f(2*n) = if n is even then 2*f(n)/3 else (f(n+1)+f(n-1))/3 for n>1, f(2*1)=1.
f(2*n) = A072403(n)/a(n) for n>1, A072403(1)=1 and a(1)=1.
LINKS
J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197; preprint. See Example 33.
E. M. Reingold and R. E. Tarjan, On a greedy heuristic for complete matching, SIAM J. Computing 10 (1981), 676-681; Semantic Scholar.
FORMULA
A072403(n) / a(n) = 2 - Sum_{k=1..n} 1 / A000244(A029837(k)). - Reinhard Zumkeller, Jan 01 2013 [Corrected by Sean A. Irvine, Sep 28 2024]
PROG
(Haskell)
import Data.Ratio ((%), denominator)
a072404 n = a072404_list !! (n-1)
a072404_list = map denominator $
scanl1 (-) $ map ((1 %) . a000244) $ a029837_list
-- Reinhard Zumkeller, Jan 01 2013
CROSSREFS
Cf. A000244, A029837, A072403 (numerators).
Sequence in context: A206700 A162349 A223022 * A222996 A268026 A268019
KEYWORD
nonn,frac
AUTHOR
Reinhard Zumkeller, Jun 16 2002
STATUS
approved